Rocksolid Light

Welcome to novaBBS (click a section below)

mail  files  register  newsreader  groups  login

Message-ID:  

Error in operator: add beer


devel / comp.theory / Re: Black box halt decider is NOT a partial decider [ Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] [ succinct ]

SubjectAuthor
* Black box halt decider is NOT a partial deciderMr Flibble
`* Black box halt decider is NOT a partial deciderChris M. Thomasson
 `* Black box halt decider is NOT a partial deciderDavid Brown
  `* Black box halt decider is NOT a partial deciderChris M. Thomasson
   +* Black box halt decider is NOT a partial deciderRichard Damon
   |`* Black box halt decider is NOT a partial deciderChris M. Thomasson
   | `* Black box halt decider is NOT a partial deciderRichard Damon
   |  `* Black box halt decider is NOT a partial deciderChris M. Thomasson
   |   +- Black box halt decider is NOT a partial deciderRichard Damon
   |   +* Black box halt decider is NOT a partial deciderBen Bacarisse
   |   |`* Black box halt decider is NOT a partial deciderChris M. Thomasson
   |   | +* Black box halt decider is NOT a partial deciderBen Bacarisse
   |   | |`* Black box halt decider is NOT a partial deciderChris M. Thomasson
   |   | | +- Black box halt decider is NOT a partial deciderRichard Damon
   |   | | `* Black box halt decider is NOT a partial deciderBen Bacarisse
   |   | |  `* Black box halt decider is NOT a partial deciderChris M. Thomasson
   |   | |   +* Black box halt decider is NOT a partial deciderAndré G. Isaak
   |   | |   |`* Black box halt decider is NOT a partial deciderChris M. Thomasson
   |   | |   | `* Black box halt decider is NOT a partial deciderMike Terry
   |   | |   |  `* Black box halt decider is NOT a partial deciderChris M. Thomasson
   |   | |   |   `* Black box halt decider is NOT a partial deciderChris M. Thomasson
   |   | |   |    +- Black box halt decider is NOT a partial deciderMike Terry
   |   | |   |    +* Black box halt decider is NOT a partial deciderBen Bacarisse
   |   | |   |    |+* Black box halt decider is NOT a partial deciderJeff Barnett
   |   | |   |    ||+- Black box halt decider is NOT a partial deciderJeff Barnett
   |   | |   |    ||`* Black box halt decider is NOT a partial deciderMike Terry
   |   | |   |    || +- Black box halt decider is NOT a partial deciderChris M. Thomasson
   |   | |   |    || `* Black box halt decider is NOT a partial deciderJeff Barnett
   |   | |   |    ||  `- Black box halt decider is NOT a partial deciderMike Terry
   |   | |   |    |`* Black box halt decider is NOT a partial deciderChris M. Thomasson
   |   | |   |    | `* Black box halt decider is NOT a partial deciderBen Bacarisse
   |   | |   |    |  `* Black box halt decider is NOT a partial deciderChris M. Thomasson
   |   | |   |    |   +- Black box halt decider is NOT a partial deciderChris M. Thomasson
   |   | |   |    |   `* Black box halt decider is NOT a partial deciderChris M. Thomasson
   |   | |   |    |    `- Black box halt decider is NOT a partial deciderChris M. Thomasson
   |   | |   |    `- Black box halt decider is NOT a partial deciderwij
   |   | |   +* Black box halt decider is NOT a partial deciderRichard Damon
   |   | |   |`* Black box halt decider is NOT a partial deciderChris M. Thomasson
   |   | |   | `* Black box halt decider is NOT a partial deciderRichard Damon
   |   | |   |  `- Black box halt decider is NOT a partial deciderChris M. Thomasson
   |   | |   `* Black box halt decider is NOT a partial deciderBen Bacarisse
   |   | |    +* Black box halt decider is NOT a partial deciderChris M. Thomasson
   |   | |    |`* Black box halt decider is NOT a partial deciderBen Bacarisse
   |   | |    | `* Black box halt decider is NOT a partial deciderChris M. Thomasson
   |   | |    |  `* Black box halt decider is NOT a partial deciderRichard Damon
   |   | |    |   `- Black box halt decider is NOT a partial deciderChris M. Thomasson
   |   | |    `* Black box halt decider is NOT a partial deciderAndré G. Isaak
   |   | |     +* Black box halt decider is NOT a partial deciderBen Bacarisse
   |   | |     |+- Black box halt decider is NOT a partial deciderAndré G. Isaak
   |   | |     |`* Black box halt decider is NOT a partial deciderMike Terry
   |   | |     | +* Black box halt decider is NOT a partial deciderBen Bacarisse
   |   | |     | |+* Black box halt decider is NOT a partial deciderAndy Walker
   |   | |     | ||`* Black box halt decider is NOT a partial deciderMike Terry
   |   | |     | || +* Black box halt decider is NOT a partial deciderMalcolm McLean
   |   | |     | || |+* Black box halt decider is NOT a partial decider [ H(P,P)==0 is always correct ]olcott
   |   | |     | || ||`- Black box halt decider is NOT a partial decider [ H(P,P)==0 isRichard Damon
   |   | |     | || |+* Black box halt decider is NOT a partial decider [ H(P,P)==0 is always correct ]olcott
   |   | |     | || ||+- Black box halt decider is NOT a partial decider [ H(P,P)==0 isAndré G. Isaak
   |   | |     | || ||+* Black box halt decider is NOT a partial decider [ H(P,P)==0 isRichard Damon
   |   | |     | || |||`* Black box halt decider is NOT a partial decider [ H(P,P)==0 isMalcolm McLean
   |   | |     | || ||| `* Black box halt decider is NOT a partial decider [ H(P,P)==0 isRichard Damon
   |   | |     | || |||  `- Black box halt decider is NOT a partial decider [ H(P,P)==0 isJeff Barnett
   |   | |     | || ||`- Black box halt decider is NOT a partial decider [ H(P,P)==0 is always correct ]Ben Bacarisse
   |   | |     | || |+* Black box halt decider is NOT a partial deciderBen Bacarisse
   |   | |     | || ||`* Black box halt decider is NOT a partial deciderMalcolm McLean
   |   | |     | || || `* Black box halt decider is NOT a partial decider [ paradox ratherolcott
   |   | |     | || ||  +- Black box halt decider is NOT a partial decider [ paradox ratherRichard Damon
   |   | |     | || ||  `* Black box halt decider is NOT a partial decider [ paradox ratherAndré G. Isaak
   |   | |     | || ||   `* Black box halt decider is NOT a partial decider [ H refutes Rice's Theorem ]olcott
   |   | |     | || ||    +- Black box halt decider is NOT a partial decider [ H refutesRichard Damon
   |   | |     | || ||    `* Black box halt decider is NOT a partial decider [ H refutesAndré G. Isaak
   |   | |     | || ||     `* Black box halt decider is NOT a partial decider [ H refutes Rice's Theorem ]olcott
   |   | |     | || ||      +* Black box halt decider is NOT a partial decider [ H refutesAndré G. Isaak
   |   | |     | || ||      |`* Black box halt decider is NOT a partial decider [ H refutesolcott
   |   | |     | || ||      | `- Black box halt decider is NOT a partial decider [ H refutesRichard Damon
   |   | |     | || ||      `* Black box halt decider is NOT a partial decider [ H refutesJeff Barnett
   |   | |     | || ||       `* Black box halt decider is NOT a partial decider [ H refutesolcott
   |   | |     | || ||        `* Black box halt decider is NOT a partial decider [ H refutesAndré G. Isaak
   |   | |     | || ||         +* Black box halt decider is NOT a partial decider [ H refutesolcott
   |   | |     | || ||         |+- Black box halt decider is NOT a partial decider [ H refutesAndré G. Isaak
   |   | |     | || ||         |`- Black box halt decider is NOT a partial decider [ H refutesRichard Damon
   |   | |     | || ||         `* Black box halt decider is NOT a partial decider [ H refutesolcott
   |   | |     | || ||          +* Black box halt decider is NOT a partial decider [ H refutesAndré G. Isaak
   |   | |     | || ||          |`* Black box halt decider is NOT a partial decider [ H refutes Rice's Theorem ]olcott
   |   | |     | || ||          | `* Black box halt decider is NOT a partial decider [ H refutesAndré G. Isaak
   |   | |     | || ||          |  `* Black box halt decider is NOT a partial decider [ H refutesolcott
   |   | |     | || ||          |   +- Black box halt decider is NOT a partial decider [ H refutesAndré G. Isaak
   |   | |     | || ||          |   +- Black box halt decider is NOT a partial decider [ H refutesRichard Damon
   |   | |     | || ||          |   `* _Black_box_halt_decider_is_NOT_a_partial_decider_[_André_doesn't_know_Rice's_Theolcott
   |   | |     | || ||          |    +* _Black_box_halt_decider_is_NOT_a_partial_decider_[André G. Isaak
   |   | |     | || ||          |    |`* _Black_box_halt_decider_is_NOT_a_partial_decider_[olcott
   |   | |     | || ||          |    | +* _Black_box_halt_decider_is_NOT_a_partial_decider_[André G. Isaak
   |   | |     | || ||          |    | |`* _Black_box_halt_decider_is_NOT_a_partial_decider_Malcolm McLean
   |   | |     | || ||          |    | | `* _André_doesn't_know_Rice's_Theorem_[_Malcolm_]olcott
   |   | |     | || ||          |    | |  +* _André_doesn't_know_Rice's_Theorem_[_MalcRichard Damon
   |   | |     | || ||          |    | |  |`* _André_doesn't_know_Rice's_Theorem_[_Malcolcott
   |   | |     | || ||          |    | |  | `* _André_doesn't_know_Rice's_Theorem_[_MalcRichard Damon
   |   | |     | || ||          |    | |  |  `* _André_doesn't_know_Rice's_Theorem_[_Malcolm_](_attention_deficit_disorder_)olcott
   |   | |     | || ||          |    | |  |   `* _André_doesn't_know_Rice's_Theorem_[_MalcRichard Damon
   |   | |     | || ||          |    | |  |    `* _André_doesn't_know_Rice's_Theorem_[_Malcolcott
   |   | |     | || ||          |    | |  |     +- _André_doesn't_know_Rice's_Theorem_[_MalcRichard Damon
   |   | |     | || ||          |    | |  |     +* _André_doesn't_know_Rice's_Theorem_[_Malcolm_](_attention_deficit_disorder_)olcott
   |   | |     | || ||          |    | |  |     `* André doesn't know Rice's Theorem [ MalcolmBen Bacarisse
   |   | |     | || ||          |    | |  +* _André_doesn't_know_Rice's_Theorem_[_MalcAndré G. Isaak
   |   | |     | || ||          |    | |  `- _André_doesn't_know_Rice's_Theorem_[_MalcJeff Barnett
   |   | |     | || ||          |    | +- _Black_box_halt_decider_is_NOT_a_partial_decider_[Richard Damon
   |   | |     | || ||          |    | `* _Black_box_halt_decider_is_NOT_a_partial_decider_[_André_doesn't_know_Rice's_Theolcott
   |   | |     | || ||          |    `- _Black_box_halt_decider_is_NOT_a_partial_decider_[Richard Damon
   |   | |     | || ||          `- Black box halt decider is NOT a partial decider [ H refutesRichard Damon
   |   | |     | || |`* Black box halt decider is NOT a partial deciderMike Terry
   |   | |     | || `- Black box halt decider is NOT a partial deciderAndy Walker
   |   | |     | |`* Black box halt decider is NOT a partial deciderMike Terry
   |   | |     | `* Black box halt decider is NOT a partial deciderwij
   |   | |     `- Black box halt decider is NOT a partial deciderChris M. Thomasson
   |   | `* Black box halt decider is NOT a partial deciderRichard Damon
   |   `* Black box halt decider is NOT a partial deciderMalcolm McLean
   `* Black box halt decider is NOT a partial deciderJeff Barnett

Pages:123456789101112131415161718192021
Re: Black box halt decider is NOT a partial decider [ Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] [ succinct ]

<87mtq189ng.fsf@bsb.me.uk>

 copy mid

https://www.novabbs.com/devel/article-flat.php?id=19329&group=comp.theory#19329

 copy link   Newsgroups: comp.theory
Path: i2pn2.org!i2pn.org!eternal-september.org!reader02.eternal-september.org!.POSTED!not-for-mail
From: ben.use...@bsb.me.uk (Ben Bacarisse)
Newsgroups: comp.theory
Subject: Re: Black box halt decider is NOT a partial decider [
Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] [
succinct ]
Date: Sun, 01 Aug 2021 16:30:43 +0100
Organization: A noiseless patient Spider
Lines: 76
Message-ID: <87mtq189ng.fsf@bsb.me.uk>
References: <20210719214640.00000dfc@reddwarf.jmc> <87pmv4ab6r.fsf@bsb.me.uk>
<JNadnQD-Ofr-SJz8nZ2dnUU7-XHNnZ2d@giganews.com>
<871r7i6n2u.fsf@bsb.me.uk>
<OqKdnROLKJ9CdJz8nZ2dnUU7-avNnZ2d@giganews.com>
<87k0la542c.fsf@bsb.me.uk>
<1NidnVPZ-NHDl5_8nZ2dnUU7-enNnZ2d@giganews.com>
<87sfzw3ao1.fsf@bsb.me.uk>
<7oKdnTjx4IC20p78nZ2dnUU7-TvNnZ2d@giganews.com>
<875yws36vt.fsf@bsb.me.uk>
<j66dnbdHrpV8_p78nZ2dnUU7-aXNnZ2d@giganews.com>
<87im0s0ydp.fsf@bsb.me.uk>
<Brqdnfehrf0Kj5n8nZ2dnUU7-X3NnZ2d@giganews.com>
<87tukblgjy.fsf@bsb.me.uk>
<qtGdnfuXs4nFOZn8nZ2dnUU7-cnNnZ2d@giganews.com>
<871r7ekugt.fsf@bsb.me.uk>
<K5-dndGZo_-VmJv8nZ2dnUU78QvNnZ2d@giganews.com>
<87czqxa0zk.fsf@bsb.me.uk>
<53d47ab9-818c-4f40-8e72-bdb76fa416een@googlegroups.com>
<87y29l8hhp.fsf@bsb.me.uk>
<99b46f6e-6017-48ec-bbd6-04dbcbd60e1an@googlegroups.com>
Mime-Version: 1.0
Content-Type: text/plain
Injection-Info: reader02.eternal-september.org; posting-host="c68c3f1263af8976689d0cd6df0e8565";
logging-data="20469"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/xnzJJwKHe+HLUmB3OMo6ShDqIouA8lFo="
Cancel-Lock: sha1:OxzusO9uGoZuWiZOf/h7+00XcIw=
sha1:OGmt1tkbOrRFOmur/jKyV15EYhY=
X-BSB-Auth: 1.0c4aef114e801a65c488.20210801163043BST.87mtq189ng.fsf@bsb.me.uk
 by: Ben Bacarisse - Sun, 1 Aug 2021 15:30 UTC

Malcolm McLean <malcolm.arthur.mclean@gmail.com> writes:

> On Sunday, 1 August 2021 at 13:41:25 UTC+1, Ben Bacarisse wrote:
>> Malcolm McLean <malcolm.ar...@gmail.com> writes:
>>
>> > However the reasons PO's halt decider fails on H_Hat(H_Hat) have
>> > got nothing to do with the invert step of Linz' proof. This is
>> > maybe interesting, but in a small way, it's not a revolutionary
>> > result which will turn computer science upside down. But it's maybe
>> > worth mentioning.
>>
>> I don't follow. H_Hat(H_Hat) halts because H(H_Hat, H_Hat) == 0 making
>> that result the wrong one. If H(H_Hat, H_Hat) returned non-zero,
>> H_Hat(H_Hat) would not halt, making that the wrong result. Whilst I
>> don't like this sort of language, H fails on H_Hat(H_Hat) precisely
>> because of how H_Hat is constructed from H.
>>
> Consider this. H_Cap (similar to H_Hat but missing the invert step);
>
> H_Cap(I)
> {
> return H(I, I):
> }
>
> Now if H is a "simulating halt decider" it must get this wrong.

I see what you mean now, though H /must/ get this wrong only if it's a
particular kind of "simulating halt decider". Some will be able to get
this case right, which is not true of the "hat" construction.

> H(I, I)
> {
> while(true)
> {
> Step(I, I);
> if (tightloopdetected())
> return Non_Halting;
> else if (haltsofitsownaccord)
> return Halting;
> }
> }
>
> The question is how we write the function tightloopdetected(). If it
> returns true then H(H_Cap, H_Cap) the H(H_Cap, H_Cap) will
> terminate. If it returns false, it wlll not.

There's a typo there but I think I get what you mean. But I don't
agree. tightloopdetected can return false (endlessly) because it's
logic is clever enough to see that haltsofitsownaccord might become
true. Of course, this all depends on the details of the logic.

You are probably right that PO's H won't have any cleverness.

> We've elimiated the "invert the result" step from Linz's proof. We
> have to insist that H is a "simulating halt decider" to achieve this.

The proof is still there, with all the same steps in it. I think you
mean there is a /different/ proof, without that step, that shows that
some naive "deciders" gets other cases wrong. I don't see why you find
that interesting, but I think that's the bottom line: you find some
things interesting that I don't.

> But that seems to be a reasonable condition. We know there are
> many properties of Turing machines that cannot be determined other
> than by stepping them.

And again I'm lost. Can you name an "interesting" property of a TM
computation that /can/ be determined by stepping it?

My guess (you'll have to confirm) is that you mean there are many
properties that we can't always determine by stepping, but stepping the
computation is the "best we can do". If so, we've had this discussion
before, and I still disagree.

--
Ben.

Re: Black box halt decider is NOT a partial decider [ Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] [ succinct ][ GIGO ]

<87h7g988a6.fsf@bsb.me.uk>

 copy mid

https://www.novabbs.com/devel/article-flat.php?id=19330&group=comp.theory#19330

 copy link   Newsgroups: comp.theory
Followup: comp.theory
Path: i2pn2.org!i2pn.org!eternal-september.org!reader02.eternal-september.org!.POSTED!not-for-mail
From: ben.use...@bsb.me.uk (Ben Bacarisse)
Newsgroups: comp.theory
Subject: Re: Black box halt decider is NOT a partial decider [
Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] [
succinct ][ GIGO ]
Followup-To: comp.theory
Date: Sun, 01 Aug 2021 17:00:17 +0100
Organization: A noiseless patient Spider
Lines: 73
Message-ID: <87h7g988a6.fsf@bsb.me.uk>
References: <20210719214640.00000dfc@reddwarf.jmc> <87pmv4ab6r.fsf@bsb.me.uk>
<JNadnQD-Ofr-SJz8nZ2dnUU7-XHNnZ2d@giganews.com>
<871r7i6n2u.fsf@bsb.me.uk>
<OqKdnROLKJ9CdJz8nZ2dnUU7-avNnZ2d@giganews.com>
<87k0la542c.fsf@bsb.me.uk>
<1NidnVPZ-NHDl5_8nZ2dnUU7-enNnZ2d@giganews.com>
<87sfzw3ao1.fsf@bsb.me.uk>
<7oKdnTjx4IC20p78nZ2dnUU7-TvNnZ2d@giganews.com>
<875yws36vt.fsf@bsb.me.uk>
<j66dnbdHrpV8_p78nZ2dnUU7-aXNnZ2d@giganews.com>
<87im0s0ydp.fsf@bsb.me.uk>
<Brqdnfehrf0Kj5n8nZ2dnUU7-X3NnZ2d@giganews.com>
<87tukblgjy.fsf@bsb.me.uk>
<qtGdnfuXs4nFOZn8nZ2dnUU7-cnNnZ2d@giganews.com>
<871r7ekugt.fsf@bsb.me.uk>
<K5-dndGZo_-VmJv8nZ2dnUU78QvNnZ2d@giganews.com>
<87czqxa0zk.fsf@bsb.me.uk>
<53d47ab9-818c-4f40-8e72-bdb76fa416een@googlegroups.com>
<87y29l8hhp.fsf@bsb.me.uk>
<LZOdnR5aLooNKpv8nZ2dnUU7-SnNnZ2d@giganews.com>
Mime-Version: 1.0
Content-Type: text/plain; charset=utf-8
Content-Transfer-Encoding: 8bit
Injection-Info: reader02.eternal-september.org; posting-host="c68c3f1263af8976689d0cd6df0e8565";
logging-data="20469"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX19n16ZKVPYB4JjbDhHUPlZMijCA2l/nqdw="
Cancel-Lock: sha1:tb/jbCLkrjXrgJxMVRMmlXHux6Y=
sha1:Pyij68V4ubj9/EnNEBhEoqFRbvE=
X-BSB-Auth: 1.6a8484dfddaf041f9634.20210801170017BST.87h7g988a6.fsf@bsb.me.uk
 by: Ben Bacarisse - Sun, 1 Aug 2021 16:00 UTC

olcott <NoOne@NoWhere.com> writes:

> On 8/1/2021 7:41 AM, Ben Bacarisse wrote:
>> Malcolm McLean <malcolm.arthur.mclean@gmail.com> writes:
>>
>>> On Sunday, 1 August 2021 at 11:54:57 UTC+1, Ben Bacarisse wrote:
>>>>
>>>> Here we can see that Ĥ applied to ⟨Ĥ⟩ halts. You can call your Ĥ's
>>>> behaviour "correct". You can call it anything you like. But it's not
>>>> "as in Linz". It does not say anything about Linz's proof. It does not
>>>> do anything people would call impossible or even interesting.
>>>>
>>> It seems to be established that H(H_Hat, H_Hat) returns "non-halting"
>>> whilst H_Hat(H_Hat) halts. So all is as Linz says it must be and no
>>> theorems are refuted. Which you would expect. If results were consistent
>>> it would have to be some cheap trick.
>> I case there is some confusion, I mean that PO's Ĥ is not an Ĥ as
>> specified in Linz. Yes, everything is in accordance with the truth as
>> laid out in Linz and, indeed, in any textbook.
>> I point this out to PO because he brings it up. He keeps posting the
>> specification of what an Ĥ, as Linz specifies it, would do:
>> Ĥ.q0 wM ⊢* Ĥ.qx wM wM ⊢* Ĥ.qn
>> if (and only if) M applied to wM does not halt.
>> He claims (or used to claim) that his Ĥ meets this specification for at
>> least the one case where wM == ⟨Ĥ⟩:
>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>> if (and only if) Ĥ applied to ⟨Ĥ⟩ does not halt.
>> To remain relevant, he /must/ keep insisting that his Ĥ meets the
>> requirements laid out in Linz, if only for this one key input.
>>
>
> Ĥ[0].q0 is taken to mean Ĥ<sub>0</sub>.q0 which is the Turing machine.
>
> Ĥ[1].q0 is taken to mean Ĥ<sub>1</sub>.q0 which is the Turing machine
> description input to Ĥ[0].q0
>
> Ĥ[2].q0 is taken to mean Ĥ<sub>2</sub>.q0 which is first copy of the
> Turing machine description input to Ĥ[0].q0
>
> Ĥ[0].q0 ⟨Ĥ⟩ ⊢* Ĥ[0].qx ⟨Ĥ[1]⟩ ⟨Ĥ[2]⟩ ⊢* Ĥ[0].qn

Ĥ[0] is Ĥ so you are confirming, yet again, that

Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qn

> It is neither a contradiction nor a paradox because there are three
> different instances of Ĥ.

I agree that this is neither a paradox nor a contradiction. It's just a
fact derived form the logic of how your Ĥ is written (the majority of
which you are keeping hidden from us).

> Because the only reason that the first instance halts is that Ĥ[0].qx
> correctly determines that its input cannot possibly ever reach its
> final state of Ĥ[1].qn or Ĥ[1].qy whether or not the simulating halt
> decider aborts its simulation of this input, we know with 100%
> perfectly justified logical certainty that the input to Ĥ[0].qx never
> halts.

We know, since you keep telling us, that Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qn. This clearly
shows that Ĥ applied to ⟨Ĥ⟩ halts. You can see the final state right
there in the line you keep posting again and again. As far as I know,
you have never disputed this fact.

As you say, this is neither a paradox nor a contradiction. It just
shows that Ĥ does not behave as Linz says it should, in the one case you
have obsessed about for 17 years. Having an H (and thus an Ĥ) that is
wrong (i.e. not "exactly and precisely as on Linz" as you once claimed)
is trivial. It is not something that anyone (except Malcolm,
apparently) would care about.

--
Ben.

Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn [ succinct ]

<TsidnfC9_pIDWJv8nZ2dnUU7-anNnZ2d@giganews.com>

 copy mid

https://www.novabbs.com/devel/article-flat.php?id=19331&group=comp.theory#19331

 copy link   Newsgroups: comp.theory comp.ai.philosophy comp.software-eng sci.philosophy
Path: i2pn2.org!i2pn.org!weretis.net!feeder6.news.weretis.net!news.snarked.org!border2.nntp.dca1.giganews.com!nntp.giganews.com!buffer2.nntp.dca1.giganews.com!news.giganews.com.POSTED!not-for-mail
NNTP-Posting-Date: Sun, 01 Aug 2021 11:02:38 -0500
Subject: Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn [ succin
ct_]
Newsgroups: comp.theory,comp.ai.philosophy,comp.software-eng,sci.philosophy
References: <20210719214640.00000dfc@reddwarf.jmc> <877dhec8wh.fsf@bsb.me.uk>
<dtudnULpgO1VVWP9nZ2dnUU7-TmdnZ2d@giganews.com> <87pmv4ab6r.fsf@bsb.me.uk>
<JNadnQD-Ofr-SJz8nZ2dnUU7-XHNnZ2d@giganews.com> <871r7i6n2u.fsf@bsb.me.uk>
<OqKdnROLKJ9CdJz8nZ2dnUU7-avNnZ2d@giganews.com> <87k0la542c.fsf@bsb.me.uk>
<1NidnVPZ-NHDl5_8nZ2dnUU7-enNnZ2d@giganews.com> <87sfzw3ao1.fsf@bsb.me.uk>
<7oKdnTjx4IC20p78nZ2dnUU7-TvNnZ2d@giganews.com> <875yws36vt.fsf@bsb.me.uk>
<j66dnbdHrpV8_p78nZ2dnUU7-aXNnZ2d@giganews.com> <87im0s0ydp.fsf@bsb.me.uk>
<Brqdnfehrf0Kj5n8nZ2dnUU7-X3NnZ2d@giganews.com> <87tukblgjy.fsf@bsb.me.uk>
<qtGdnfuXs4nFOZn8nZ2dnUU7-cnNnZ2d@giganews.com> <871r7ekugt.fsf@bsb.me.uk>
<K5-dndGZo_-VmJv8nZ2dnUU78QvNnZ2d@giganews.com> <87czqxa0zk.fsf@bsb.me.uk>
<53d47ab9-818c-4f40-8e72-bdb76fa416een@googlegroups.com>
<87y29l8hhp.fsf@bsb.me.uk>
<99b46f6e-6017-48ec-bbd6-04dbcbd60e1an@googlegroups.com>
From: NoO...@NoWhere.com (olcott)
Date: Sun, 1 Aug 2021 11:02:38 -0500
User-Agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64; rv:78.0) Gecko/20100101
Thunderbird/78.12.0
MIME-Version: 1.0
In-Reply-To: <99b46f6e-6017-48ec-bbd6-04dbcbd60e1an@googlegroups.com>
Content-Type: text/plain; charset=utf-8; format=flowed
Content-Language: en-US
Content-Transfer-Encoding: 7bit
Message-ID: <TsidnfC9_pIDWJv8nZ2dnUU7-anNnZ2d@giganews.com>
Lines: 105
X-Usenet-Provider: http://www.giganews.com
X-Trace: sv3-z21d90qVzHhsYTQ0lhOVjPQRcZDIbvoFej4Dd6692F+r22juCtDvdbx9DbYin3dkWKjTX2YqYNXchc5!57Q1qE/1EtsjkOj6RWzSS+lRaIQk9M7NHs2+7BfbCM+GQhlo+mEeO0PLHEMg/3J7ZOsImR4LLA==
X-Complaints-To: abuse@giganews.com
X-DMCA-Notifications: http://www.giganews.com/info/dmca.html
X-Abuse-and-DMCA-Info: Please be sure to forward a copy of ALL headers
X-Abuse-and-DMCA-Info: Otherwise we will be unable to process your complaint properly
X-Postfilter: 1.3.40
X-Original-Bytes: 5892
 by: olcott - Sun, 1 Aug 2021 16:02 UTC

On 8/1/2021 9:25 AM, Malcolm McLean wrote:
> On Sunday, 1 August 2021 at 13:41:25 UTC+1, Ben Bacarisse wrote:
>> Malcolm McLean <malcolm.ar...@gmail.com> writes:
>>
>>> However the reasons PO's halt decider fails on H_Hat(H_Hat) have got
>>> nothing to do with the invert step of Linz' proof. This is maybe interesting,
>>> but in a small way, it's not a revolutionary result which will turn computer
>>> science upside down. But it's maybe worth mentioning.
>> I don't follow. H_Hat(H_Hat) halts because H(H_Hat, H_Hat) == 0 making
>> that result the wrong one. If H(H_Hat, H_Hat) returned non-zero,
>> H_Hat(H_Hat) would not halt, making that the wrong result. Whilst I
>> don't like this sort of language, H fails on H_Hat(H_Hat) precisely
>> because of how H_Hat is constructed from H.
>>
> Consider this. H_Cap (similar to H_Hat but missing the invert step);
>
> H_Cap(I)
> {
> return H(I, I):
> }
>
> Now if H is a "simulating halt decider" it must get this wrong. H is (skeleton
> code)
>
> H(I, I)
> {
> while(true)
> {
> Step(I, I);
> if (tightloopdetected())
> return Non_Halting;
> else if (haltsofitsownaccord)
> return Halting;
> }
> }
>
> The question is how we write the function tightloopdetected(). If it returns
> true then H(H_Cap, H_Cap) the H(H_Cap, H_Cap) will terminate. If
> it returns false, it wlll not. So H can never make the right decision for H_Cap(H_Cap).
>

Some errors were corrected and the rest was adapted to x86utm.

u32 HH(I, I)
{ HERE:
{
if (H(I, I) == 0)
return 0;
else
return 1;
}
goto HERE;
}

u32 H_Cap(I)
{ return HH(I, I);
}

int main()
{ Output("Input_Halts = ", H((u32)H_Cap, (u32)H_Cap));
}

Begin Local Halt Decider Simulation at Machine Address:d02
....[00000d02][00211915][00211919] 55 push ebp
....[00000d03][00211915][00211919] 8bec mov ebp,esp
....[00000d05][00211915][00211919] 8b4508 mov eax,[ebp+08]
....[00000d08][00211911][00000d02] 50 push eax
....[00000d09][00211911][00000d02] 8b4d08 mov ecx,[ebp+08]
....[00000d0c][0021190d][00000d02] 51 push ecx
....[00000d0d][00211909][00000d12] e8c0ffffff call 00000cd2
....[00000cd2][00211905][00211915] 55 push ebp
....[00000cd3][00211905][00211915] 8bec mov ebp,esp
....[00000cd5][00211905][00211915] 8b4508 mov eax,[ebp+08]
....[00000cd8][00211901][00000d02] 50 push eax
....[00000cd9][00211901][00000d02] 8b4d08 mov ecx,[ebp+08]
....[00000cdc][002118fd][00000d02] 51 push ecx
....[00000cdd][002118f9][00000ce2] e8e0fdffff call 00000ac2
....[00000d02][0025c33d][0025c341] 55 push ebp
....[00000d03][0025c33d][0025c341] 8bec mov ebp,esp
....[00000d05][0025c33d][0025c341] 8b4508 mov eax,[ebp+08]
....[00000d08][0025c339][00000d02] 50 push eax
....[00000d09][0025c339][00000d02] 8b4d08 mov ecx,[ebp+08]
....[00000d0c][0025c335][00000d02] 51 push ecx
....[00000d0d][0025c331][00000d12] e8c0ffffff call 00000cd2
Local Halt Decider: Infinite Recursion Detected Simulation Stopped

Input_Halts = 0

Proving that the above code is decided correctly.

> We've elimiated the "invert the result" step from Linz's proof. We have to
> insist that H is a "simulating halt decider" to achieve this. But that seems
> to be a reasonable condition. We know there are many properties of Turing
> machines that cannot be determined other than by stepping them.
>

--
Copyright 2021 Pete Olcott

"Great spirits have always encountered violent opposition from mediocre
minds." Einstein

Re: Black box halt decider is NOT a partial decider [ Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] [ succinct ]

<50dfd889-9418-48d0-a20d-1d1f2c029c42n@googlegroups.com>

 copy mid

https://www.novabbs.com/devel/article-flat.php?id=19332&group=comp.theory#19332

 copy link   Newsgroups: comp.theory
X-Received: by 2002:a37:a544:: with SMTP id o65mr12056715qke.68.1627843273441;
Sun, 01 Aug 2021 11:41:13 -0700 (PDT)
X-Received: by 2002:a25:c5d4:: with SMTP id v203mr16842323ybe.295.1627843273304;
Sun, 01 Aug 2021 11:41:13 -0700 (PDT)
Path: i2pn2.org!i2pn.org!weretis.net!feeder8.news.weretis.net!proxad.net!feeder1-2.proxad.net!209.85.160.216.MISMATCH!news-out.google.com!nntp.google.com!postnews.google.com!google-groups.googlegroups.com!not-for-mail
Newsgroups: comp.theory
Date: Sun, 1 Aug 2021 11:41:13 -0700 (PDT)
In-Reply-To: <87mtq189ng.fsf@bsb.me.uk>
Injection-Info: google-groups.googlegroups.com; posting-host=81.143.231.9; posting-account=Dz2zqgkAAADlK5MFu78bw3ab-BRFV4Qn
NNTP-Posting-Host: 81.143.231.9
References: <20210719214640.00000dfc@reddwarf.jmc> <87pmv4ab6r.fsf@bsb.me.uk>
<JNadnQD-Ofr-SJz8nZ2dnUU7-XHNnZ2d@giganews.com> <871r7i6n2u.fsf@bsb.me.uk>
<OqKdnROLKJ9CdJz8nZ2dnUU7-avNnZ2d@giganews.com> <87k0la542c.fsf@bsb.me.uk>
<1NidnVPZ-NHDl5_8nZ2dnUU7-enNnZ2d@giganews.com> <87sfzw3ao1.fsf@bsb.me.uk>
<7oKdnTjx4IC20p78nZ2dnUU7-TvNnZ2d@giganews.com> <875yws36vt.fsf@bsb.me.uk>
<j66dnbdHrpV8_p78nZ2dnUU7-aXNnZ2d@giganews.com> <87im0s0ydp.fsf@bsb.me.uk>
<Brqdnfehrf0Kj5n8nZ2dnUU7-X3NnZ2d@giganews.com> <87tukblgjy.fsf@bsb.me.uk>
<qtGdnfuXs4nFOZn8nZ2dnUU7-cnNnZ2d@giganews.com> <871r7ekugt.fsf@bsb.me.uk>
<K5-dndGZo_-VmJv8nZ2dnUU78QvNnZ2d@giganews.com> <87czqxa0zk.fsf@bsb.me.uk>
<53d47ab9-818c-4f40-8e72-bdb76fa416een@googlegroups.com> <87y29l8hhp.fsf@bsb.me.uk>
<99b46f6e-6017-48ec-bbd6-04dbcbd60e1an@googlegroups.com> <87mtq189ng.fsf@bsb.me.uk>
User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <50dfd889-9418-48d0-a20d-1d1f2c029c42n@googlegroups.com>
Subject: Re: Black box halt decider is NOT a partial decider
[ Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] [ succinct ]
From: malcolm....@gmail.com (Malcolm McLean)
Injection-Date: Sun, 01 Aug 2021 18:41:13 +0000
Content-Type: text/plain; charset="UTF-8"
 by: Malcolm McLean - Sun, 1 Aug 2021 18:41 UTC

On Sunday, 1 August 2021 at 16:30:46 UTC+1, Ben Bacarisse wrote:
> Malcolm McLean <malcolm.ar...@gmail.com> writes:
>
> > We've elimiated the "invert the result" step from Linz's proof. We
> > have to insist that H is a "simulating halt decider" to achieve this.
> The proof is still there, with all the same steps in it. I think you
> mean there is a /different/ proof, without that step, that shows that
> some naive "deciders" gets other cases wrong. I don't see why you find
> that interesting, but I think that's the bottom line: you find some
> things interesting that I don't.
>
Sure, there's a different proof, inspired by Linz's, but with the "invert
the result" step removed. It only applies to naive simulating deciders.
So to make it into a proof of general interest, we've got to show that
a naive simulating decider can't be bettered by any other type of
decider.
>
> > But that seems to be a reasonable condition. We know there are
> > many properties of Turing machines that cannot be determined other
> > than by stepping them.
> And again I'm lost. Can you name an "interesting" property of a TM
> computation that /can/ be determined by stepping it?
>
Take its busy beaver score, for example. You might object that even a
stepping scorer can't always detect when a machine won't halt. So just
add a limit, which grows with then number of states to keep the set
infinite. Busy beaver score before either a halt or m * N states steps.
>
> My guess (you'll have to confirm) is that you mean there are many
> properties that we can't always determine by stepping, but stepping the
> computation is the "best we can do". If so, we've had this discussion
> before, and I still disagree.
>
Yes, that's a reasonable summary.

Re: Black box halt decider is NOT a partial decider [ Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] [ succinct ]

<87bl6h7yqy.fsf@bsb.me.uk>

 copy mid

https://www.novabbs.com/devel/article-flat.php?id=19333&group=comp.theory#19333

 copy link   Newsgroups: comp.theory
Path: i2pn2.org!i2pn.org!eternal-september.org!reader02.eternal-september.org!.POSTED!not-for-mail
From: ben.use...@bsb.me.uk (Ben Bacarisse)
Newsgroups: comp.theory
Subject: Re: Black box halt decider is NOT a partial decider [
Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] [
succinct ]
Date: Sun, 01 Aug 2021 20:26:13 +0100
Organization: A noiseless patient Spider
Lines: 26
Message-ID: <87bl6h7yqy.fsf@bsb.me.uk>
References: <20210719214640.00000dfc@reddwarf.jmc> <871r7i6n2u.fsf@bsb.me.uk>
<OqKdnROLKJ9CdJz8nZ2dnUU7-avNnZ2d@giganews.com>
<87k0la542c.fsf@bsb.me.uk>
<1NidnVPZ-NHDl5_8nZ2dnUU7-enNnZ2d@giganews.com>
<87sfzw3ao1.fsf@bsb.me.uk>
<7oKdnTjx4IC20p78nZ2dnUU7-TvNnZ2d@giganews.com>
<875yws36vt.fsf@bsb.me.uk>
<j66dnbdHrpV8_p78nZ2dnUU7-aXNnZ2d@giganews.com>
<87im0s0ydp.fsf@bsb.me.uk>
<Brqdnfehrf0Kj5n8nZ2dnUU7-X3NnZ2d@giganews.com>
<87tukblgjy.fsf@bsb.me.uk>
<qtGdnfuXs4nFOZn8nZ2dnUU7-cnNnZ2d@giganews.com>
<871r7ekugt.fsf@bsb.me.uk>
<K5-dndGZo_-VmJv8nZ2dnUU78QvNnZ2d@giganews.com>
<87czqxa0zk.fsf@bsb.me.uk>
<53d47ab9-818c-4f40-8e72-bdb76fa416een@googlegroups.com>
<87y29l8hhp.fsf@bsb.me.uk>
<99b46f6e-6017-48ec-bbd6-04dbcbd60e1an@googlegroups.com>
<87mtq189ng.fsf@bsb.me.uk>
<50dfd889-9418-48d0-a20d-1d1f2c029c42n@googlegroups.com>
Mime-Version: 1.0
Content-Type: text/plain
Injection-Info: reader02.eternal-september.org; posting-host="c68c3f1263af8976689d0cd6df0e8565";
logging-data="21491"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX18wfP8XRxbXHHn1gMDY5f7WNtgrV+OGDaE="
Cancel-Lock: sha1:uZkrk6UjAekMxdjo2G9VAZUHtK4=
sha1:jb860K26cWY1FoHNhKg0Y6EBjX8=
X-BSB-Auth: 1.527bd8a48ce25359bf06.20210801202613BST.87bl6h7yqy.fsf@bsb.me.uk
 by: Ben Bacarisse - Sun, 1 Aug 2021 19:26 UTC

Malcolm McLean <malcolm.arthur.mclean@gmail.com> writes:

> On Sunday, 1 August 2021 at 16:30:46 UTC+1, Ben Bacarisse wrote:
>> Malcolm McLean <malcolm.ar...@gmail.com> writes:
>>
>> > We've elimiated the "invert the result" step from Linz's proof. We
>> > have to insist that H is a "simulating halt decider" to achieve this.
>> The proof is still there, with all the same steps in it. I think you
>> mean there is a /different/ proof, without that step, that shows that
>> some naive "deciders" gets other cases wrong. I don't see why you find
>> that interesting, but I think that's the bottom line: you find some
>> things interesting that I don't.
>>
> Sure, there's a different proof, inspired by Linz's, but with the "invert
> the result" step removed. It only applies to naive simulating deciders.
> So to make it into a proof of general interest, we've got to show that
> a naive simulating decider can't be bettered by any other type of
> decider.

I don't see a way to get from "some very simple simulating TMs get even
simple cases wrong" to anything of interest. I can't even see how to
define a "simulating decider" without making it obvious how to construct
a better one.

--
Ben.

Re: Black box halt decider is NOT a partial decider [ Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] [ succinct ]

<cPadnTZbe-5oZJv8nZ2dnUU7-bednZ2d@giganews.com>

 copy mid

https://www.novabbs.com/devel/article-flat.php?id=19334&group=comp.theory#19334

 copy link   Newsgroups: comp.theory comp.ai.philosophy comp.software-eng sci.math.symbolic
Path: i2pn2.org!i2pn.org!weretis.net!feeder8.news.weretis.net!news.uzoreto.com!tr1.eu1.usenetexpress.com!feeder.usenetexpress.com!tr2.iad1.usenetexpress.com!border1.nntp.dca1.giganews.com!nntp.giganews.com!buffer1.nntp.dca1.giganews.com!buffer2.nntp.dca1.giganews.com!news.giganews.com.POSTED!not-for-mail
NNTP-Posting-Date: Sun, 01 Aug 2021 14:45:57 -0500
Subject: Re:_Black_box_halt_decider_is_NOT_a_partial_decider_[ Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] [ succinct ]
Newsgroups: comp.theory,comp.ai.philosophy,comp.software-eng,sci.math.symbolic
References: <20210719214640.00000dfc@reddwarf.jmc> <87pmv4ab6r.fsf@bsb.me.uk> <JNadnQD-Ofr-SJz8nZ2dnUU7-XHNnZ2d@giganews.com> <871r7i6n2u.fsf@bsb.me.uk> <OqKdnROLKJ9CdJz8nZ2dnUU7-avNnZ2d@giganews.com> <87k0la542c.fsf@bsb.me.uk> <1NidnVPZ-NHDl5_8nZ2dnUU7-enNnZ2d@giganews.com> <87sfzw3ao1.fsf@bsb.me.uk> <7oKdnTjx4IC20p78nZ2dnUU7-TvNnZ2d@giganews.com> <875yws36vt.fsf@bsb.me.uk> <j66dnbdHrpV8_p78nZ2dnUU7-aXNnZ2d@giganews.com> <87im0s0ydp.fsf@bsb.me.uk> <Brqdnfehrf0Kj5n8nZ2dnUU7-X3NnZ2d@giganews.com> <87tukblgjy.fsf@bsb.me.uk> <qtGdnfuXs4nFOZn8nZ2dnUU7-cnNnZ2d@giganews.com> <871r7ekugt.fsf@bsb.me.uk> <K5-dndGZo_-VmJv8nZ2dnUU78QvNnZ2d@giganews.com> <87czqxa0zk.fsf@bsb.me.uk> <53d47ab9-818c-4f40-8e72-bdb76fa416een@googlegroups.com> <87y29l8hhp.fsf@bsb.me.uk> <99b46f6e-6017-48ec-bbd6-04dbcbd60e1an@googlegroups.com> <87mtq189ng.fsf@bsb.me.uk> <50dfd889-9418-48d0-a20d-1d1f2c029c42n@googlegroups.com>
From: NoO...@NoWhere.com (olcott)
Date: Sun, 1 Aug 2021 14:45:57 -0500
User-Agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64; rv:78.0) Gecko/20100101 Thunderbird/78.12.0
MIME-Version: 1.0
In-Reply-To: <50dfd889-9418-48d0-a20d-1d1f2c029c42n@googlegroups.com>
Content-Type: text/plain; charset=utf-8; format=flowed
Content-Language: en-US
Content-Transfer-Encoding: 7bit
Message-ID: <cPadnTZbe-5oZJv8nZ2dnUU7-bednZ2d@giganews.com>
Lines: 96
X-Usenet-Provider: http://www.giganews.com
X-Trace: sv3-Mr1rXn/vUIkGKSrx0ik9oE7nKemy8di9lUvodoMGAv/vJyzZ39mPnIiEIK4++Ti3UbLln/UTu4/JhsS!AbM9y4OlYPUcKzTHnvkV3osS9Oby7ydDkNMKWZVBa8ehYfpAU2fmTDbXQQ8PSeA0401+yvzMkQ==
X-Complaints-To: abuse@giganews.com
X-DMCA-Notifications: http://www.giganews.com/info/dmca.html
X-Abuse-and-DMCA-Info: Please be sure to forward a copy of ALL headers
X-Abuse-and-DMCA-Info: Otherwise we will be unable to process your complaint properly
X-Postfilter: 1.3.40
X-Original-Bytes: 6038
 by: olcott - Sun, 1 Aug 2021 19:45 UTC

On 8/1/2021 1:41 PM, Malcolm McLean wrote:
> On Sunday, 1 August 2021 at 16:30:46 UTC+1, Ben Bacarisse wrote:
>> Malcolm McLean <malcolm.ar...@gmail.com> writes:
>>
>>> We've elimiated the "invert the result" step from Linz's proof. We
>>> have to insist that H is a "simulating halt decider" to achieve this.
>> The proof is still there, with all the same steps in it. I think you
>> mean there is a /different/ proof, without that step, that shows that
>> some naive "deciders" gets other cases wrong. I don't see why you find
>> that interesting, but I think that's the bottom line: you find some
>> things interesting that I don't.
>>
> Sure, there's a different proof, inspired by Linz's, but with the "invert
> the result" step removed. It only applies to naive simulating deciders.
> So to make it into a proof of general interest, we've got to show that
> a naive simulating decider can't be bettered by any other type of
> decider.
>>
>>> But that seems to be a reasonable condition. We know there are
>>> many properties of Turing machines that cannot be determined other
>>> than by stepping them.
>> And again I'm lost. Can you name an "interesting" property of a TM
>> computation that /can/ be determined by stepping it?
>>
> Take its busy beaver score, for example. You might object that even a
> stepping scorer can't always detect when a machine won't halt. So just
> add a limit, which grows with then number of states to keep the set
> infinite. Busy beaver score before either a halt or m * N states steps.
>>
>> My guess (you'll have to confirm) is that you mean there are many
>> properties that we can't always determine by stepping, but stepping the
>> computation is the "best we can do". If so, we've had this discussion
>> before, and I still disagree.
>>
> Yes, that's a reasonable summary.
>

>

Some errors were corrected and the rest was adapted to x86utm.

u32 HH(I, I)
{ HERE:
{
if (H(I, I) == 0)
return 0;
else
return 1;
}
goto HERE;
}

u32 H_Cap(I)
{ return HH(I, I);
}

int main()
{ Output("Input_Halts = ", H((u32)H_Cap, (u32)H_Cap));
}

Begin Local Halt Decider Simulation at Machine Address:d02
....[00000d02][00211915][00211919] 55 push ebp
....[00000d03][00211915][00211919] 8bec mov ebp,esp
....[00000d05][00211915][00211919] 8b4508 mov eax,[ebp+08]
....[00000d08][00211911][00000d02] 50 push eax
....[00000d09][00211911][00000d02] 8b4d08 mov ecx,[ebp+08]
....[00000d0c][0021190d][00000d02] 51 push ecx
....[00000d0d][00211909][00000d12] e8c0ffffff call 00000cd2
....[00000cd2][00211905][00211915] 55 push ebp
....[00000cd3][00211905][00211915] 8bec mov ebp,esp
....[00000cd5][00211905][00211915] 8b4508 mov eax,[ebp+08]
....[00000cd8][00211901][00000d02] 50 push eax
....[00000cd9][00211901][00000d02] 8b4d08 mov ecx,[ebp+08]
....[00000cdc][002118fd][00000d02] 51 push ecx
....[00000cdd][002118f9][00000ce2] e8e0fdffff call 00000ac2
....[00000d02][0025c33d][0025c341] 55 push ebp
....[00000d03][0025c33d][0025c341] 8bec mov ebp,esp
....[00000d05][0025c33d][0025c341] 8b4508 mov eax,[ebp+08]
....[00000d08][0025c339][00000d02] 50 push eax
....[00000d09][0025c339][00000d02] 8b4d08 mov ecx,[ebp+08]
....[00000d0c][0025c335][00000d02] 51 push ecx
....[00000d0d][0025c331][00000d12] e8c0ffffff call 00000cd2
Local Halt Decider: Infinite Recursion Detected Simulation Stopped

Input_Halts = 0

Proving that the above code is decided correctly.

--
Copyright 2021 Pete Olcott

"Great spirits have always encountered violent opposition from mediocre
minds." Einstein

Re: Black box halt decider is NOT a partial decider [ Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] [ succinct ]

<HtDNI.133084$h8.109373@fx47.iad>

 copy mid

https://www.novabbs.com/devel/article-flat.php?id=19335&group=comp.theory#19335

 copy link   Newsgroups: comp.theory
Path: i2pn2.org!i2pn.org!weretis.net!feeder8.news.weretis.net!ecngs!feeder2.ecngs.de!178.20.174.213.MISMATCH!feeder1.feed.usenet.farm!feed.usenet.farm!peer02.ams4!peer.am4.highwinds-media.com!peer02.iad!feed-me.highwinds-media.com!news.highwinds-media.com!fx47.iad.POSTED!not-for-mail
Subject: Re:_Black_box_halt_decider_is_NOT_a_partial_decider_[
Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] [ succinct
]
Newsgroups: comp.theory
References: <20210719214640.00000dfc@reddwarf.jmc> <87pmv4ab6r.fsf@bsb.me.uk>
<JNadnQD-Ofr-SJz8nZ2dnUU7-XHNnZ2d@giganews.com> <871r7i6n2u.fsf@bsb.me.uk>
<OqKdnROLKJ9CdJz8nZ2dnUU7-avNnZ2d@giganews.com> <87k0la542c.fsf@bsb.me.uk>
<1NidnVPZ-NHDl5_8nZ2dnUU7-enNnZ2d@giganews.com> <87sfzw3ao1.fsf@bsb.me.uk>
<7oKdnTjx4IC20p78nZ2dnUU7-TvNnZ2d@giganews.com> <875yws36vt.fsf@bsb.me.uk>
<j66dnbdHrpV8_p78nZ2dnUU7-aXNnZ2d@giganews.com> <87im0s0ydp.fsf@bsb.me.uk>
<Brqdnfehrf0Kj5n8nZ2dnUU7-X3NnZ2d@giganews.com> <87tukblgjy.fsf@bsb.me.uk>
<qtGdnfuXs4nFOZn8nZ2dnUU7-cnNnZ2d@giganews.com> <871r7ekugt.fsf@bsb.me.uk>
<K5-dndGZo_-VmJv8nZ2dnUU78QvNnZ2d@giganews.com> <87czqxa0zk.fsf@bsb.me.uk>
<53d47ab9-818c-4f40-8e72-bdb76fa416een@googlegroups.com>
<87y29l8hhp.fsf@bsb.me.uk>
<99b46f6e-6017-48ec-bbd6-04dbcbd60e1an@googlegroups.com>
<87mtq189ng.fsf@bsb.me.uk>
<50dfd889-9418-48d0-a20d-1d1f2c029c42n@googlegroups.com>
<cPadnTZbe-5oZJv8nZ2dnUU7-bednZ2d@giganews.com>
From: Rich...@Damon-Family.org (Richard Damon)
User-Agent: Mozilla/5.0 (Macintosh; Intel Mac OS X 10.15; rv:78.0)
Gecko/20100101 Thunderbird/78.12.0
MIME-Version: 1.0
In-Reply-To: <cPadnTZbe-5oZJv8nZ2dnUU7-bednZ2d@giganews.com>
Content-Type: text/plain; charset=utf-8
Content-Language: en-US
Content-Transfer-Encoding: 8bit
Lines: 105
Message-ID: <HtDNI.133084$h8.109373@fx47.iad>
X-Complaints-To: abuse@easynews.com
Organization: Forte - www.forteinc.com
X-Complaints-Info: Please be sure to forward a copy of ALL headers otherwise we will be unable to process your complaint properly.
Date: Sun, 1 Aug 2021 13:28:23 -0700
X-Received-Bytes: 6458
 by: Richard Damon - Sun, 1 Aug 2021 20:28 UTC

On 8/1/21 12:45 PM, olcott wrote:
> On 8/1/2021 1:41 PM, Malcolm McLean wrote:
>> On Sunday, 1 August 2021 at 16:30:46 UTC+1, Ben Bacarisse wrote:
>>> Malcolm McLean <malcolm.ar...@gmail.com> writes:
>>>
>>>> We've elimiated the "invert the result" step from Linz's proof. We
>>>> have to insist that H is a "simulating halt decider" to achieve this.
>>> The proof is still there, with all the same steps in it. I think you
>>> mean there is a /different/ proof, without that step, that shows that
>>> some naive "deciders" gets other cases wrong. I don't see why you find
>>> that interesting, but I think that's the bottom line: you find some
>>> things interesting that I don't.
>>>
>> Sure, there's a different proof, inspired by Linz's, but with the "invert
>> the result" step removed. It only applies to naive simulating deciders.
>> So to make it into a proof of general interest, we've got to show that
>> a naive simulating decider can't be bettered by any other type of
>> decider.
>>>
>>>> But that seems to be a reasonable condition. We know there are
>>>> many properties of Turing machines that cannot be determined other
>>>> than by stepping them.
>>> And again I'm lost. Can you name an "interesting" property of a TM
>>> computation that /can/ be determined by stepping it?
>>>
>> Take its busy beaver score, for example. You might object that even a
>> stepping scorer can't always detect when a machine won't halt. So just
>> add a limit, which grows with then number of states  to keep the set
>> infinite. Busy beaver score before either a halt or m * N states steps.
>>>
>>> My guess (you'll have to confirm) is that you mean there are many
>>> properties that we can't always determine by stepping, but stepping the
>>> computation is the "best we can do". If so, we've had this discussion
>>> before, and I still disagree.
>>>
>> Yes, that's a reasonable summary.
>>
>
>>
>
> Some errors were corrected and the rest was adapted to x86utm.
>
> u32 HH(I, I)
> {
> HERE:
>   {
>     if (H(I, I) == 0)
>       return 0;
>     else
>       return 1;
>    }
>   goto HERE;
> }
>
> u32 H_Cap(I)
> {
>   return HH(I, I);
> }
>
> int main()
> {
>   Output("Input_Halts = ", H((u32)H_Cap, (u32)H_Cap));
> }
>
> Begin Local Halt Decider Simulation at Machine Address:d02
> ...[00000d02][00211915][00211919] 55          push ebp
> ...[00000d03][00211915][00211919] 8bec        mov ebp,esp
> ...[00000d05][00211915][00211919] 8b4508      mov eax,[ebp+08]
> ...[00000d08][00211911][00000d02] 50          push eax
> ...[00000d09][00211911][00000d02] 8b4d08      mov ecx,[ebp+08]
> ...[00000d0c][0021190d][00000d02] 51          push ecx
> ...[00000d0d][00211909][00000d12] e8c0ffffff  call 00000cd2
> ...[00000cd2][00211905][00211915] 55          push ebp
> ...[00000cd3][00211905][00211915] 8bec        mov ebp,esp
> ...[00000cd5][00211905][00211915] 8b4508      mov eax,[ebp+08]
> ...[00000cd8][00211901][00000d02] 50          push eax
> ...[00000cd9][00211901][00000d02] 8b4d08      mov ecx,[ebp+08]
> ...[00000cdc][002118fd][00000d02] 51          push ecx
> ...[00000cdd][002118f9][00000ce2] e8e0fdffff  call 00000ac2
> ...[00000d02][0025c33d][0025c341] 55          push ebp
> ...[00000d03][0025c33d][0025c341] 8bec        mov ebp,esp
> ...[00000d05][0025c33d][0025c341] 8b4508      mov eax,[ebp+08]
> ...[00000d08][0025c339][00000d02] 50          push eax
> ...[00000d09][0025c339][00000d02] 8b4d08      mov ecx,[ebp+08]
> ...[00000d0c][0025c335][00000d02] 51          push ecx
> ...[00000d0d][0025c331][00000d12] e8c0ffffff  call 00000cd2
> Local Halt Decider: Infinite Recursion Detected Simulation Stopped
>
> Input_Halts = 0
>
> Proving that the above code is decided correctly.
>

So, the issue isn't that H^ is contrary to H, just that it uses H?

Or, is H just non-halting on any recursive use of it?

It is clear that running H_Cap(H_Cap) by itself will return as H will
abort its simulation, return 0, HH return 0, and H_Cap returns 0.

You have lost the argument that there is no right answer, as if H does
return a 1 saying that it halts, it will be right.

The only conclusion I can make out of this is that you are just trying
to define that any 'recursive' use of H is considered non-halting.

Re: Black box halt decider is NOT a partial decider [ Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] ( Are you game ? )

<6eOdnaoMUdZN_pr8nZ2dnUU7-cPNnZ2d@giganews.com>

 copy mid

https://www.novabbs.com/devel/article-flat.php?id=19354&group=comp.theory#19354

 copy link   Newsgroups: comp.theory comp.ai.philosophy comp.software-eng sci.math.symbolic
Path: i2pn2.org!i2pn.org!aioe.org!news.uzoreto.com!tr3.eu1.usenetexpress.com!feeder.usenetexpress.com!tr2.iad1.usenetexpress.com!border1.nntp.dca1.giganews.com!nntp.giganews.com!buffer1.nntp.dca1.giganews.com!news.giganews.com.POSTED!not-for-mail
NNTP-Posting-Date: Sun, 01 Aug 2021 22:17:36 -0500
Subject: Re:_Black_box_halt_decider_is_NOT_a_partial_decider_[ Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] ( Are you game_?_)
Newsgroups: comp.theory,comp.ai.philosophy,comp.software-eng,sci.math.symbolic
References: <20210719214640.00000dfc@reddwarf.jmc> <eOadnfv1CNxEEGD9nZ2dnUU78RPNnZ2d@brightview.co.uk> <4826ab33-061b-472e-a1a5-e2ded35ecd82n@googlegroups.com> <Ob2dneXfOsPHVGD9nZ2dnUU78aHNnZ2d@brightview.co.uk> <tOudnQr4N_JfUGD9nZ2dnUU78fHNnZ2d@brightview.co.uk> <877dhec8wh.fsf@bsb.me.uk> <dtudnULpgO1VVWP9nZ2dnUU7-TmdnZ2d@giganews.com> <87pmv4ab6r.fsf@bsb.me.uk> <JNadnQD-Ofr-SJz8nZ2dnUU7-XHNnZ2d@giganews.com> <871r7i6n2u.fsf@bsb.me.uk> <OqKdnROLKJ9CdJz8nZ2dnUU7-avNnZ2d@giganews.com> <87k0la542c.fsf@bsb.me.uk> <x5mdnTC66uNJip_8nZ2dnUU7-aWdnZ2d@giganews.com> <87mtq438ge.fsf@bsb.me.uk> <PbednTcmR4_Mw578nZ2dnUU78WvNnZ2d@giganews.com> <87tukc12yh.fsf@bsb.me.uk> <e6OdnW_rdvusk5n8nZ2dnUU7-dPNnZ2d@giganews.com> <875ywrmwsr.fsf@bsb.me.uk> <GtmdnfBrysPrAZn8nZ2dnUU7-L_NnZ2d@giganews.com> <874kcakv3d.fsf@bsb.me.uk> <-M-dnfsXl4WvWpj8nZ2dnUU7-IGdnZ2d@giganews.com> <87im0pa1pp.fsf@bsb.me.uk>
From: NoO...@NoWhere.com (olcott)
Date: Sun, 1 Aug 2021 22:17:35 -0500
User-Agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64; rv:78.0) Gecko/20100101 Thunderbird/78.12.0
MIME-Version: 1.0
In-Reply-To: <87im0pa1pp.fsf@bsb.me.uk>
Content-Type: text/plain; charset=utf-8; format=flowed
Content-Language: en-US
Content-Transfer-Encoding: 8bit
Message-ID: <6eOdnaoMUdZN_pr8nZ2dnUU7-cPNnZ2d@giganews.com>
Lines: 70
X-Usenet-Provider: http://www.giganews.com
X-Trace: sv3-fiPzqI5zZXvR5yXvYUycENupvkAaW0nzpXdgIMzU/upLOcSnxj73WuHRq4z3cHeY36j9ndXk0Z8wM4t!IR5/jAEtpphjoU0MkjtfNGw/CLMEwwW1n7LVMZSXiA8kMKwcxnsy69cLqluZEITDD2kOuPhTWQ==
X-Complaints-To: abuse@giganews.com
X-DMCA-Notifications: http://www.giganews.com/info/dmca.html
X-Abuse-and-DMCA-Info: Please be sure to forward a copy of ALL headers
X-Abuse-and-DMCA-Info: Otherwise we will be unable to process your complaint properly
X-Postfilter: 1.3.40
X-Original-Bytes: 5255
 by: olcott - Mon, 2 Aug 2021 03:17 UTC

On 8/1/2021 5:39 AM, Ben Bacarisse wrote:
> olcott <NoOne@NoWhere.com> writes:
>
>> On 7/31/2021 4:54 PM, Ben Bacarisse wrote:
>>> olcott <NoOne@NoWhere.com> writes:
>>>
>>>> It matters not what I had.
>>> Because you can't justify it the honest debate you claim to want.
>>>
>>>> It only matters what I have.
>>> I.e. nothing of any interest. You make it plain in a previous reply
>>> that you've had nothing of interest going right back to the original
>>> deceptive claim.
>>>
>>>> If you are sincere about an honest dialogue then we must quit focusing
>>>> on details of obsolete technology.
>>> And yet you skipped the big picture part:
>>>
>>>>> (5) You said you had "an H that decides (Ĥ, Ĥ)". What decision did your
>>>>> Dec 2018 code come to about "(Ĥ, Ĥ)"?
>>>>
>>>> The 2018 version Halts(H_Hat, H_Hat)==0 in the exact same way that
>>>> H(P,P)==0 now except that the never halting criteria is much more
>>>> elaborate. The initial criteria was very crude.
>>>
>>> Ah, so you never had H and H_Hat that do anything that anyone would say
>>> is impossible. Had you said, back in Dec 2018, "I have C code such that
>>> H(H_Hat, H_Hat) == 0 but H_Hat(H_Hat) halts" no one would have been
>>> interested.
>>
>> If you are sincere about an honest dialogue then we must quit focusing
>> on details of obsolete technology.
>
> Ah, an honest dialogue requires me to ignore your past deception? Well,
> I can accommodate that: you /currently/ don't have anything that anyone
> would consider to be impossible or even interesting. An H/H_Hat pair
> such that H(H_Hat, H_Hat) == 0 and H_Hat(H_Hat) halts is of no interest
> to anyone. Is that better?
>

When H is a simulating partial halt decider and the halt decider
embedded in Ĥ at Ĥ.qx is a simulating halt decider then:

It is the case that the input to H(P,P) and the input to Ĥ(⟨Ĥ⟩) cannot
possibly ever reach their final state and must have their simulation
aborted to prevent the infinite execution of P and Ĥ.

Let's have an honest dialogue about that.

>>> I think you owe everyone an apology. Even if there was no indent to
>>> deceive, your words back then did everything possible to suggest some
>>> impossible Turing machine. And you wouldn't say, until recently, even
>>> when explicitly asked, what decision H came to. It was fishy from the
>>> start.
>
> You still owe everyone an apology. Neither Turing machines nor C code
> are obsolete technology. If you really had what you falsely claimed to
> have had, posting it at any time in the last 30 months would have
> settled the matter. It still would, but you either never had anything
> at all or you are too embarrassed to post what it was.
>

The technology that I had in 2018 is obsolete and not relevant to an
honest dialogue about the technology that I currently have.

--
Copyright 2021 Pete Olcott

"Great spirits have always encountered violent opposition from mediocre
minds." Einstein

Re: Black box halt decider is NOT a partial decider [ Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] ( Are you game ? )

<1LJNI.97822$VU3.31489@fx46.iad>

 copy mid

https://www.novabbs.com/devel/article-flat.php?id=19357&group=comp.theory#19357

 copy link   Newsgroups: comp.theory
Path: i2pn2.org!i2pn.org!paganini.bofh.team!news.dns-netz.com!news.freedyn.net!newsfeed.xs4all.nl!newsfeed9.news.xs4all.nl!news-out.netnews.com!news.alt.net!fdc2.netnews.com!peer01.ams1!peer.ams1.xlned.com!news.xlned.com!peer03.iad!feed-me.highwinds-media.com!news.highwinds-media.com!fx46.iad.POSTED!not-for-mail
Subject: Re:_Black_box_halt_decider_is_NOT_a_partial_decider_[
Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] ( Are you g
ame_?_)
Newsgroups: comp.theory
References: <20210719214640.00000dfc@reddwarf.jmc>
<eOadnfv1CNxEEGD9nZ2dnUU78RPNnZ2d@brightview.co.uk>
<4826ab33-061b-472e-a1a5-e2ded35ecd82n@googlegroups.com>
<Ob2dneXfOsPHVGD9nZ2dnUU78aHNnZ2d@brightview.co.uk>
<tOudnQr4N_JfUGD9nZ2dnUU78fHNnZ2d@brightview.co.uk>
<877dhec8wh.fsf@bsb.me.uk> <dtudnULpgO1VVWP9nZ2dnUU7-TmdnZ2d@giganews.com>
<87pmv4ab6r.fsf@bsb.me.uk> <JNadnQD-Ofr-SJz8nZ2dnUU7-XHNnZ2d@giganews.com>
<871r7i6n2u.fsf@bsb.me.uk> <OqKdnROLKJ9CdJz8nZ2dnUU7-avNnZ2d@giganews.com>
<87k0la542c.fsf@bsb.me.uk> <x5mdnTC66uNJip_8nZ2dnUU7-aWdnZ2d@giganews.com>
<87mtq438ge.fsf@bsb.me.uk> <PbednTcmR4_Mw578nZ2dnUU78WvNnZ2d@giganews.com>
<87tukc12yh.fsf@bsb.me.uk> <e6OdnW_rdvusk5n8nZ2dnUU7-dPNnZ2d@giganews.com>
<875ywrmwsr.fsf@bsb.me.uk> <GtmdnfBrysPrAZn8nZ2dnUU7-L_NnZ2d@giganews.com>
<874kcakv3d.fsf@bsb.me.uk> <-M-dnfsXl4WvWpj8nZ2dnUU7-IGdnZ2d@giganews.com>
<87im0pa1pp.fsf@bsb.me.uk> <6eOdnaoMUdZN_pr8nZ2dnUU7-cPNnZ2d@giganews.com>
From: Rich...@Damon-Family.org (Richard Damon)
User-Agent: Mozilla/5.0 (Macintosh; Intel Mac OS X 10.15; rv:78.0)
Gecko/20100101 Thunderbird/78.12.0
MIME-Version: 1.0
In-Reply-To: <6eOdnaoMUdZN_pr8nZ2dnUU7-cPNnZ2d@giganews.com>
Content-Type: text/plain; charset=utf-8
Content-Language: en-US
Content-Transfer-Encoding: 8bit
Lines: 35
Message-ID: <1LJNI.97822$VU3.31489@fx46.iad>
X-Complaints-To: abuse@easynews.com
Organization: Forte - www.forteinc.com
X-Complaints-Info: Please be sure to forward a copy of ALL headers otherwise we will be unable to process your complaint properly.
Date: Sun, 1 Aug 2021 20:36:27 -0700
X-Received-Bytes: 3309
 by: Richard Damon - Mon, 2 Aug 2021 03:36 UTC

> When H is a simulating partial halt decider and the halt decider
> embedded in Ĥ at Ĥ.qx is a simulating halt decider then:
>
> It is the case that the input to H(P,P) and the input to Ĥ(⟨Ĥ⟩) cannot
> possibly ever reach their final state and must have their simulation
> aborted to prevent the infinite execution of P and Ĥ.
>

The key is that 'the input' doesn't need to reach the halting state,
since the input ISN'T a Turing Machine, just a description.

What matters is what the Turing Machine that input represents, and THAT
Halts.

The input will also halt if given to a REAL UTM, i.e. one that won't
abort its input.

The fact that the algorithm of H aborts its simulation before its
simulation reachs its Halting state proves NOTHING.

The fact that the decider uses UNSOUND logic says that its 'proof' is
invalid. It makes the error of assuming that the copy of H that it is
simulating will NEVER abort its simulation, when it would if allowed to
run long enough, as is demonstrated in the trace of the actual run of
H^(H^).

> Let's have an honest dialogue about that.

Yes. Please look at the ACTUAL facts.

What statement do I make that is incorrect and you can PROVE to be wrong.

EVERYTHING I have said is based on the ACTUAL definitions, not what sees
to be by the 'meaning' of the words.

Re: Black box halt decider is NOT a partial decider [ Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] [ succinct ]

<woudnXWBxPba95r8nZ2dnUU78ffNnZ2d@giganews.com>

 copy mid

https://www.novabbs.com/devel/article-flat.php?id=19360&group=comp.theory#19360

 copy link   Newsgroups: comp.theory comp.ai.philosophy comp.software-eng sci.math.symbolic
Path: i2pn2.org!i2pn.org!eternal-september.org!reader02.eternal-september.org!border1.nntp.ams1.giganews.com!nntp.giganews.com!buffer1.nntp.ams1.giganews.com!news.giganews.com.POSTED!not-for-mail
NNTP-Posting-Date: Sun, 01 Aug 2021 22:45:10 -0500
Subject: Re:_Black_box_halt_decider_is_NOT_a_partial_decider_[
Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] [ succinct
]
Newsgroups: comp.theory,comp.ai.philosophy,comp.software-eng,sci.math.symbolic
References: <20210719214640.00000dfc@reddwarf.jmc>
<Ob2dneXfOsPHVGD9nZ2dnUU78aHNnZ2d@brightview.co.uk>
<tOudnQr4N_JfUGD9nZ2dnUU78fHNnZ2d@brightview.co.uk>
<877dhec8wh.fsf@bsb.me.uk> <dtudnULpgO1VVWP9nZ2dnUU7-TmdnZ2d@giganews.com>
<87pmv4ab6r.fsf@bsb.me.uk> <JNadnQD-Ofr-SJz8nZ2dnUU7-XHNnZ2d@giganews.com>
<871r7i6n2u.fsf@bsb.me.uk> <OqKdnROLKJ9CdJz8nZ2dnUU7-avNnZ2d@giganews.com>
<87k0la542c.fsf@bsb.me.uk> <1NidnVPZ-NHDl5_8nZ2dnUU7-enNnZ2d@giganews.com>
<87sfzw3ao1.fsf@bsb.me.uk> <7oKdnTjx4IC20p78nZ2dnUU7-TvNnZ2d@giganews.com>
<875yws36vt.fsf@bsb.me.uk> <j66dnbdHrpV8_p78nZ2dnUU7-aXNnZ2d@giganews.com>
<87im0s0ydp.fsf@bsb.me.uk> <Brqdnfehrf0Kj5n8nZ2dnUU7-X3NnZ2d@giganews.com>
<87tukblgjy.fsf@bsb.me.uk> <qtGdnfuXs4nFOZn8nZ2dnUU7-cnNnZ2d@giganews.com>
<871r7ekugt.fsf@bsb.me.uk> <K5-dndGZo_-VmJv8nZ2dnUU78QvNnZ2d@giganews.com>
<87czqxa0zk.fsf@bsb.me.uk>
From: NoO...@NoWhere.com (olcott)
Date: Sun, 1 Aug 2021 22:45:09 -0500
User-Agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64; rv:78.0) Gecko/20100101
Thunderbird/78.12.0
MIME-Version: 1.0
In-Reply-To: <87czqxa0zk.fsf@bsb.me.uk>
Content-Type: text/plain; charset=utf-8; format=flowed
Content-Language: en-US
Content-Transfer-Encoding: 8bit
Message-ID: <woudnXWBxPba95r8nZ2dnUU78ffNnZ2d@giganews.com>
Lines: 173
X-Usenet-Provider: http://www.giganews.com
X-Trace: sv3-MIkUcNVx0tzNwByDWcRVjKi5vAxP9IERetoHRmZp5qSI/jvS659s8VHISS7B9/oa81RumkEyhuaOF6i!zbTqHiCCBh+gVHUHxOx8B6nAdipIGx25G6i/LoGil+inkQRv2IkVpQmmT6Z5S0VlGOHLOEPSsg==
X-Complaints-To: abuse@giganews.com
X-DMCA-Notifications: http://www.giganews.com/info/dmca.html
X-Abuse-and-DMCA-Info: Please be sure to forward a copy of ALL headers
X-Abuse-and-DMCA-Info: Otherwise we will be unable to process your complaint properly
X-Postfilter: 1.3.40
X-Original-Bytes: 9570
 by: olcott - Mon, 2 Aug 2021 03:45 UTC

On 8/1/2021 5:54 AM, Ben Bacarisse wrote:
> olcott <NoOne@NoWhere.com> writes:
>
>> On 7/31/2021 5:08 PM, Ben Bacarisse wrote:
>>> olcott <NoOne@NoWhere.com> writes:
>>>
>>>> On 7/30/2021 2:58 PM, Ben Bacarisse wrote:
>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>
>>>>>> On 7/30/2021 7:39 AM, Ben Bacarisse wrote:
>>>>>
>>>>>>> Any chance you will now say if
>>>>>>>
>>>>>>>> Ĥ.qx(⟨Ĥ⟩, ⟨Ĥ⟩)
>>>>>>>
>>>>>>> transitions to Ĥ.qn or Ĥ.qy? If you find this question difficult,
>>>>>>> please ask for some help in understanding it.
>>>>>>
>>>>>> Ĥ.qx(⟨Ĥ⟩, ⟨Ĥ⟩) transitions to Ĥ.qn
>>>>>
>>>>> An answer. Thank you.
>>>>>
>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>>>>
>>>>> For Ĥ to be "exactly and precisely as in Linz" this, then, is the clause
>>>>> that applies to your H and Ĥ:
>>>>
>>>> There is no H in the relevant last paragraph of the Linz proof that
>>>> forms the basis for the Linz conclusion.
>>> Distraction. Everything you ignore below is about the proof and refers
>>> only to Ĥ.
>>>
>>>>>>>>>>>>>>>> Ĥ.q0 wM ⊢* Ĥ.qx wM wM ⊢* Ĥ.qn
>>>>>>>>>>>>>>>> if M applied to wM does not halt
>>>>>
>>>>> so Ĥ (M) applied to ⟨Ĥ⟩ (wM) does not halt, but you have just told me
>>>>> that it does. That is what this full (but abbreviated) state transition
>>>>> sequence means:
>>>>>
>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>>>>
>>>>> Which is it?
>>>>
>>>> Ĥ0.q0 copies its input ⟨Ĥ1⟩ to ⟨Ĥ2⟩ then Ĥ0.qx simulates Ĥ1 with the
>>>> ⟨Ĥ2⟩ copy then
>>>> Ĥ1.q0 copies its input ⟨Ĥ2⟩ to ⟨Ĥ3⟩ then Ĥ1.qx simulates Ĥ2 with the
>>>> ⟨Ĥ3⟩ copy then
>>>> Ĥ2.q0 copies its input ⟨Ĥ3⟩ to ⟨Ĥ4⟩ then Ĥ2.qx simulates Ĥ3 with the
>>>> ⟨Ĥ4⟩ copy then ...
>>> This is an abuse of the notation (but I know what you mean). There is
>>> no Ĥ1 or Ĥ2. If you think it helps to show which copy of ⟨Ĥ⟩ your
>>> simulating "decider" is either running and/or currently looking at, you
>>> need to come up with a notation that does that.
>>
>> A better notation is what I have in my PDF actual subscripts but
>> people here tel me that their newsreader makes sure to totally ignore
>> posts with HTML so that do even see the post at all.
>
> I am happy you have a notation you like. Are you prepared to address
> that fact that your H^ is not "as in Linz"?
>

My Ĥ is exactly the Linz Ĥ with the additional elaboration that the
second wildcard state transition ⊢* is defined to be a simulating halt
decider. The Linz ⊢* explicitly allows for this without diverging from
the Linz template at all.

Ĥ.q0 wM ⊢* Ĥ.qx wM wM ⊢*

>>> At least I know what
>>> this "math poem" means, because you've been saying this "it's a
>>> simulator until" stuff for years.
>>>
>>>> The outermost Ĥ0.qx correctly decides that its input: (⟨Ĥ1⟩, ⟨Ĥ2⟩)
>>>> can't possibly ever reach its final state. Then it transitions to
>>>> Ĥ0.qn causing the outermost Ĥ0 to halt.
>>> Apart from the bad notation, yes. All those copies and tests and
>>> eventual deciding are neatly summed up in the last ⊢* Ĥ.qn of
>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>>
>>>> Because the outermost Ĥ0.qx did not decide that Ĥ0 would never halt
>>>> and it is self evident that its input: (⟨Ĥ1⟩, ⟨Ĥ2⟩) can't possibly
>>>> ever reach its final state there is no contradiction or paradox and it
>>>> decided correctly.
>>> You are free to define "decide correctly" in any way you like provided
>>> you are honest about it. But you hooked people in by saying that your Ĥ
>>> is "exactly and precisely as in Linz", and you quoted, even now, what
>>> Linz has to say about such TMs:
>>> Ĥ.q0 wM ⊢* Ĥ.qx wM wM ⊢* Ĥ.qn
>>> if M applied to wM does not halt
>>> This is your quote. You brought it up. You claimed your Ĥ was as Linz
>>> states -- that Ĥ.q0 wM ⊢* Ĥ.qn if and only if M applied to wM does not
>>> halt. Linz makes no exceptions based on why the transitions from Ĥ.q0
>>> wM to Ĥ.qn occur. Linz does not say
>>> Ĥ.q0 wM ⊢* Ĥ.qx wM wM ⊢* Ĥ.qn
>>> if M applied to wM does not halt or if M applied wM only halts
>>> because...
>>> Are you now saying that your TM was not "as in Linz"? (You should,
>>> because you've admitted that elsewhere.)
>>
>> Ĥ[0] is to be interpreted to mean Ĥ<sub>0</sub>
>> [0] Means the actual Turing machine and not a TM description.
>> [1] Means the first TM description parameter
>> [2] Means a copy of the the first TM description parameter
>>
>> Now I am saying that when the actual unmodified Linz Ĥ is understood
>> to have a UTM/Halt-Decider at Ĥ[0].qx that this Ĥ[0].qx does correctly
>> decide that its input: (⟨Ĥ[1]⟩, ⟨Ĥ[2]⟩) can't possibly ever reach its
>> final state of Ĥ[1].qn or Ĥ[2].qn, therefore we know that its input
>> never halts therefore we know that a state transition from Ĥ[0].qx to
>> Ĥ0.qn is necessarily correct.
>
> We all know you are declaring that to be correct. Here's why your Ĥ is
> not "as in Linz". Linz requires that
>
> Ĥ.q0 wM ⊢* Ĥ.qx wM wM ⊢* Ĥ.qn
> if M applied to wM does not halt
>
> Any Ĥ that eventually transitions to Ĥ.qn on input wM must do so
> if, and only if, the encoded M applied to wM does not halt. But you've
> given us a case where your Ĥ is not like this:
>
> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>

And when we eliminate the fallacy of equivocation error we have

Ĥ[0].q0 ⟨Ĥ⟩ ⊢* Ĥ[0].qx ⟨Ĥ[1]⟩ ⟨Ĥ[2]⟩ ⊢* Ĥ[0].qn

The way that you do it when your twin bother commits a crime that makes
you guilty.

Ĥ[0].q0 ⟨Ĥ[1]⟩ only halts because the simulation of the
the input to Ĥ[0].qx ⟨Ĥ[1]⟩ ⟨Ĥ[2]⟩ was aborted.

(a) The simulation of the input to Ĥ[0].qx ⟨Ĥ[1]⟩ ⟨Ĥ[2]⟩
was aborted because neither ⟨Ĥ[1]⟩ nor ⟨Ĥ[2]⟩ could
ever possibly reach their final states.

(b) Because neither ⟨Ĥ[1]⟩ nor ⟨Ĥ[2]⟩ could ever possibly reach
their final states we know that they never halt.

(c) Because they never halt we know that Ĥ[0].qx correctly decided
that its input never halts.

This is the same as: X > Y & Y > Z therefore X > Z
I do seem to have a correct chain of inference.
I do not think that you can point to any error in
this chain of inference.

In an honest dialogue when you would disagree that a
chain of inference derives a correct conclusion you
would point to a specific error in this chain of inference.

What is the error in (a)(b)(c) ?

> Here we can see that Ĥ applied to ⟨Ĥ⟩ halts. You can call your Ĥ's
> behaviour "correct". You can call it anything you like. But it's not
> "as in Linz". It does not say anything about Linz's proof. It does not
> do anything people would call impossible or even interesting.
>
> Presumably, you will simply explain, yet again, why you choose to call
> it correct. You might even, yet again, quote the symbols from Linz that
> don't apply to your Ĥ in order to make you posts seem relevant.
>

--
Copyright 2021 Pete Olcott

"Great spirits have always encountered violent opposition from mediocre
minds." Einstein

Re: Black box halt decider is NOT a partial decider [ Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] [ succinct ]

<ktidnbuI6J5g8Zr8nZ2dnUU7-XfNnZ2d@giganews.com>

 copy mid

https://www.novabbs.com/devel/article-flat.php?id=19361&group=comp.theory#19361

 copy link   Newsgroups: comp.theory comp.software-eng
Path: i2pn2.org!i2pn.org!aioe.org!feeder1.feed.usenet.farm!feed.usenet.farm!tr1.eu1.usenetexpress.com!feeder.usenetexpress.com!tr3.iad1.usenetexpress.com!border1.nntp.dca1.giganews.com!nntp.giganews.com!buffer1.nntp.dca1.giganews.com!news.giganews.com.POSTED!not-for-mail
NNTP-Posting-Date: Sun, 01 Aug 2021 22:56:45 -0500
Subject: Re:_Black_box_halt_decider_is_NOT_a_partial_decider_[ Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] [ succinct ]
Newsgroups: comp.theory,comp.software-eng
References: <20210719214640.00000dfc@reddwarf.jmc> <Ob2dneXfOsPHVGD9nZ2dnUU78aHNnZ2d@brightview.co.uk> <tOudnQr4N_JfUGD9nZ2dnUU78fHNnZ2d@brightview.co.uk> <877dhec8wh.fsf@bsb.me.uk> <dtudnULpgO1VVWP9nZ2dnUU7-TmdnZ2d@giganews.com> <87pmv4ab6r.fsf@bsb.me.uk> <JNadnQD-Ofr-SJz8nZ2dnUU7-XHNnZ2d@giganews.com> <871r7i6n2u.fsf@bsb.me.uk> <OqKdnROLKJ9CdJz8nZ2dnUU7-avNnZ2d@giganews.com> <87k0la542c.fsf@bsb.me.uk> <1NidnVPZ-NHDl5_8nZ2dnUU7-enNnZ2d@giganews.com> <87sfzw3ao1.fsf@bsb.me.uk> <7oKdnTjx4IC20p78nZ2dnUU7-TvNnZ2d@giganews.com> <875yws36vt.fsf@bsb.me.uk> <j66dnbdHrpV8_p78nZ2dnUU7-aXNnZ2d@giganews.com> <87im0s0ydp.fsf@bsb.me.uk> <Brqdnfehrf0Kj5n8nZ2dnUU7-X3NnZ2d@giganews.com> <87tukblgjy.fsf@bsb.me.uk> <qtGdnfuXs4nFOZn8nZ2dnUU7-cnNnZ2d@giganews.com> <871r7ekugt.fsf@bsb.me.uk> <K5-dndGZo_-VmJv8nZ2dnUU78QvNnZ2d@giganews.com> <87czqxa0zk.fsf@bsb.me.uk>
From: NoO...@NoWhere.com (olcott)
Date: Sun, 1 Aug 2021 22:56:45 -0500
User-Agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64; rv:78.0) Gecko/20100101 Thunderbird/78.12.0
MIME-Version: 1.0
In-Reply-To: <87czqxa0zk.fsf@bsb.me.uk>
Content-Type: text/plain; charset=utf-8; format=flowed
Content-Language: en-US
Content-Transfer-Encoding: 8bit
Message-ID: <ktidnbuI6J5g8Zr8nZ2dnUU7-XfNnZ2d@giganews.com>
Lines: 166
X-Usenet-Provider: http://www.giganews.com
X-Trace: sv3-VchVLQPHODg4RlcMJ1c60RWhGkVb18FHQ/p8TAZiuBDUTWjE+Q5+Zd4BFzRcD8s3/RLz6rU6Dgp3nbm!3cH806+sRBUOzLfLgoBdQlOjIBWWZd/eqgFGWtuIayno9bJzFKQejWUfyV7hXMppVna365yFIA==
X-Complaints-To: abuse@giganews.com
X-DMCA-Notifications: http://www.giganews.com/info/dmca.html
X-Abuse-and-DMCA-Info: Please be sure to forward a copy of ALL headers
X-Abuse-and-DMCA-Info: Otherwise we will be unable to process your complaint properly
X-Postfilter: 1.3.40
X-Original-Bytes: 9318
 by: olcott - Mon, 2 Aug 2021 03:56 UTC

On 8/1/2021 5:54 AM, Ben Bacarisse wrote:
> olcott <NoOne@NoWhere.com> writes:
>
>> On 7/31/2021 5:08 PM, Ben Bacarisse wrote:
>>> olcott <NoOne@NoWhere.com> writes:
>>>
>>>> On 7/30/2021 2:58 PM, Ben Bacarisse wrote:
>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>
>>>>>> On 7/30/2021 7:39 AM, Ben Bacarisse wrote:
>>>>>
>>>>>>> Any chance you will now say if
>>>>>>>
>>>>>>>> Ĥ.qx(⟨Ĥ⟩, ⟨Ĥ⟩)
>>>>>>>
>>>>>>> transitions to Ĥ.qn or Ĥ.qy? If you find this question difficult,
>>>>>>> please ask for some help in understanding it.
>>>>>>
>>>>>> Ĥ.qx(⟨Ĥ⟩, ⟨Ĥ⟩) transitions to Ĥ.qn
>>>>>
>>>>> An answer. Thank you.
>>>>>
>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>>>>
>>>>> For Ĥ to be "exactly and precisely as in Linz" this, then, is the clause
>>>>> that applies to your H and Ĥ:
>>>>
>>>> There is no H in the relevant last paragraph of the Linz proof that
>>>> forms the basis for the Linz conclusion.
>>> Distraction. Everything you ignore below is about the proof and refers
>>> only to Ĥ.
>>>
>>>>>>>>>>>>>>>> Ĥ.q0 wM ⊢* Ĥ.qx wM wM ⊢* Ĥ.qn
>>>>>>>>>>>>>>>> if M applied to wM does not halt
>>>>>
>>>>> so Ĥ (M) applied to ⟨Ĥ⟩ (wM) does not halt, but you have just told me
>>>>> that it does. That is what this full (but abbreviated) state transition
>>>>> sequence means:
>>>>>
>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>>>>
>>>>> Which is it?
>>>>
>>>> Ĥ0.q0 copies its input ⟨Ĥ1⟩ to ⟨Ĥ2⟩ then Ĥ0.qx simulates Ĥ1 with the
>>>> ⟨Ĥ2⟩ copy then
>>>> Ĥ1.q0 copies its input ⟨Ĥ2⟩ to ⟨Ĥ3⟩ then Ĥ1.qx simulates Ĥ2 with the
>>>> ⟨Ĥ3⟩ copy then
>>>> Ĥ2.q0 copies its input ⟨Ĥ3⟩ to ⟨Ĥ4⟩ then Ĥ2.qx simulates Ĥ3 with the
>>>> ⟨Ĥ4⟩ copy then ...
>>> This is an abuse of the notation (but I know what you mean). There is
>>> no Ĥ1 or Ĥ2. If you think it helps to show which copy of ⟨Ĥ⟩ your
>>> simulating "decider" is either running and/or currently looking at, you
>>> need to come up with a notation that does that.
>>
>> A better notation is what I have in my PDF actual subscripts but
>> people here tel me that their newsreader makes sure to totally ignore
>> posts with HTML so that do even see the post at all.
>
> I am happy you have a notation you like. Are you prepared to address
> that fact that your H^ is not "as in Linz"?
>
>>> At least I know what
>>> this "math poem" means, because you've been saying this "it's a
>>> simulator until" stuff for years.
>>>
>>>> The outermost Ĥ0.qx correctly decides that its input: (⟨Ĥ1⟩, ⟨Ĥ2⟩)
>>>> can't possibly ever reach its final state. Then it transitions to
>>>> Ĥ0.qn causing the outermost Ĥ0 to halt.
>>> Apart from the bad notation, yes. All those copies and tests and
>>> eventual deciding are neatly summed up in the last ⊢* Ĥ.qn of
>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>>
>>>> Because the outermost Ĥ0.qx did not decide that Ĥ0 would never halt
>>>> and it is self evident that its input: (⟨Ĥ1⟩, ⟨Ĥ2⟩) can't possibly
>>>> ever reach its final state there is no contradiction or paradox and it
>>>> decided correctly.
>>> You are free to define "decide correctly" in any way you like provided
>>> you are honest about it. But you hooked people in by saying that your Ĥ
>>> is "exactly and precisely as in Linz", and you quoted, even now, what
>>> Linz has to say about such TMs:
>>> Ĥ.q0 wM ⊢* Ĥ.qx wM wM ⊢* Ĥ.qn
>>> if M applied to wM does not halt
>>> This is your quote. You brought it up. You claimed your Ĥ was as Linz
>>> states -- that Ĥ.q0 wM ⊢* Ĥ.qn if and only if M applied to wM does not
>>> halt. Linz makes no exceptions based on why the transitions from Ĥ.q0
>>> wM to Ĥ.qn occur. Linz does not say
>>> Ĥ.q0 wM ⊢* Ĥ.qx wM wM ⊢* Ĥ.qn
>>> if M applied to wM does not halt or if M applied wM only halts
>>> because...
>>> Are you now saying that your TM was not "as in Linz"? (You should,
>>> because you've admitted that elsewhere.)
>>
>> Ĥ[0] is to be interpreted to mean Ĥ<sub>0</sub>
>> [0] Means the actual Turing machine and not a TM description.
>> [1] Means the first TM description parameter
>> [2] Means a copy of the the first TM description parameter
>>
>> Now I am saying that when the actual unmodified Linz Ĥ is understood
>> to have a UTM/Halt-Decider at Ĥ[0].qx that this Ĥ[0].qx does correctly
>> decide that its input: (⟨Ĥ[1]⟩, ⟨Ĥ[2]⟩) can't possibly ever reach its
>> final state of Ĥ[1].qn or Ĥ[2].qn, therefore we know that its input
>> never halts therefore we know that a state transition from Ĥ[0].qx to
>> Ĥ0.qn is necessarily correct.
>
> We all know you are declaring that to be correct. Here's why your Ĥ is
> not "as in Linz". Linz requires that
>
> Ĥ.q0 wM ⊢* Ĥ.qx wM wM ⊢* Ĥ.qn
> if M applied to wM does not halt
>
> Any Ĥ that eventually transitions to Ĥ.qn on input wM must do so
> if, and only if, the encoded M applied to wM does not halt. But you've
> given us a case where your Ĥ is not like this:
>
> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn

*This did not show up in my other news server so I am pointing it again*

And when we eliminate the fallacy of equivocation error we have

Ĥ[0].q0 ⟨Ĥ⟩ ⊢* Ĥ[0].qx ⟨Ĥ[1]⟩ ⟨Ĥ[2]⟩ ⊢* Ĥ[0].qn

The way that you do it when your twin bother commits a crime that makes
you guilty.

Ĥ[0].q0 ⟨Ĥ[1]⟩ only halts because the simulation of the
the input to Ĥ[0].qx ⟨Ĥ[1]⟩ ⟨Ĥ[2]⟩ was aborted.

(a) The simulation of the input to Ĥ[0].qx ⟨Ĥ[1]⟩ ⟨Ĥ[2]⟩
was aborted because neither ⟨Ĥ[1]⟩ nor ⟨Ĥ[2]⟩ could
ever possibly reach their final states.

(b) Because neither ⟨Ĥ[1]⟩ nor ⟨Ĥ[2]⟩ could ever possibly reach
their final states we know that they never halt.

(c) Because they never halt we know that Ĥ[0].qx correctly decided
that its input never halts.

This is the same as: X > Y & Y > Z therefore X > Z
I do seem to have a correct chain of inference.
I do not think that you can point to any error in
this chain of inference.

In an honest dialogue when you would disagree that a
chain of inference derives a correct conclusion you
would point to a specific error in this chain of inference.

What is the error in (a)(b)(c) ?

> Here we can see that Ĥ applied to ⟨Ĥ⟩ halts. You can call your Ĥ's
> behaviour "correct". You can call it anything you like. But it's not
> "as in Linz". It does not say anything about Linz's proof. It does not
> do anything people would call impossible or even interesting.
>
> Presumably, you will simply explain, yet again, why you choose to call
> it correct. You might even, yet again, quote the symbols from Linz that
> don't apply to your Ĥ in order to make you posts seem relevant.
>

--
Copyright 2021 Pete Olcott

"Great spirits have always encountered violent opposition from mediocre
minds." Einstein

Re: Black box halt decider is NOT a partial decider [ Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] [ succinct ]

<69LNI.98022$VU3.50110@fx46.iad>

 copy mid

https://www.novabbs.com/devel/article-flat.php?id=19363&group=comp.theory#19363

 copy link   Newsgroups: comp.theory
Path: i2pn2.org!i2pn.org!aioe.org!feeder1.feed.usenet.farm!feed.usenet.farm!peer03.ams4!peer.am4.highwinds-media.com!peer01.iad!feed-me.highwinds-media.com!news.highwinds-media.com!fx46.iad.POSTED!not-for-mail
Subject: Re:_Black_box_halt_decider_is_NOT_a_partial_decider_[
Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] [ succinct
]
Newsgroups: comp.theory
References: <20210719214640.00000dfc@reddwarf.jmc>
<Ob2dneXfOsPHVGD9nZ2dnUU78aHNnZ2d@brightview.co.uk>
<tOudnQr4N_JfUGD9nZ2dnUU78fHNnZ2d@brightview.co.uk>
<877dhec8wh.fsf@bsb.me.uk> <dtudnULpgO1VVWP9nZ2dnUU7-TmdnZ2d@giganews.com>
<87pmv4ab6r.fsf@bsb.me.uk> <JNadnQD-Ofr-SJz8nZ2dnUU7-XHNnZ2d@giganews.com>
<871r7i6n2u.fsf@bsb.me.uk> <OqKdnROLKJ9CdJz8nZ2dnUU7-avNnZ2d@giganews.com>
<87k0la542c.fsf@bsb.me.uk> <1NidnVPZ-NHDl5_8nZ2dnUU7-enNnZ2d@giganews.com>
<87sfzw3ao1.fsf@bsb.me.uk> <7oKdnTjx4IC20p78nZ2dnUU7-TvNnZ2d@giganews.com>
<875yws36vt.fsf@bsb.me.uk> <j66dnbdHrpV8_p78nZ2dnUU7-aXNnZ2d@giganews.com>
<87im0s0ydp.fsf@bsb.me.uk> <Brqdnfehrf0Kj5n8nZ2dnUU7-X3NnZ2d@giganews.com>
<87tukblgjy.fsf@bsb.me.uk> <qtGdnfuXs4nFOZn8nZ2dnUU7-cnNnZ2d@giganews.com>
<871r7ekugt.fsf@bsb.me.uk> <K5-dndGZo_-VmJv8nZ2dnUU78QvNnZ2d@giganews.com>
<87czqxa0zk.fsf@bsb.me.uk> <woudnXWBxPba95r8nZ2dnUU78ffNnZ2d@giganews.com>
From: Rich...@Damon-Family.org (Richard Damon)
User-Agent: Mozilla/5.0 (Macintosh; Intel Mac OS X 10.15; rv:78.0)
Gecko/20100101 Thunderbird/78.12.0
MIME-Version: 1.0
In-Reply-To: <woudnXWBxPba95r8nZ2dnUU78ffNnZ2d@giganews.com>
Content-Type: text/plain; charset=utf-8
Content-Language: en-US
Content-Transfer-Encoding: 8bit
Lines: 220
Message-ID: <69LNI.98022$VU3.50110@fx46.iad>
X-Complaints-To: abuse@easynews.com
Organization: Forte - www.forteinc.com
X-Complaints-Info: Please be sure to forward a copy of ALL headers otherwise we will be unable to process your complaint properly.
Date: Sun, 1 Aug 2021 22:12:33 -0700
X-Received-Bytes: 11200
 by: Richard Damon - Mon, 2 Aug 2021 05:12 UTC

On 8/1/21 8:45 PM, olcott wrote:
> On 8/1/2021 5:54 AM, Ben Bacarisse wrote:
>> olcott <NoOne@NoWhere.com> writes:
>>
>>> On 7/31/2021 5:08 PM, Ben Bacarisse wrote:
>>>> olcott <NoOne@NoWhere.com> writes:
>>>>
>>>>> On 7/30/2021 2:58 PM, Ben Bacarisse wrote:
>>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>>
>>>>>>> On 7/30/2021 7:39 AM, Ben Bacarisse wrote:
>>>>>>
>>>>>>>> Any chance you will now say if
>>>>>>>>
>>>>>>>>>      Ĥ.qx(⟨Ĥ⟩, ⟨Ĥ⟩)
>>>>>>>>
>>>>>>>> transitions to Ĥ.qn or Ĥ.qy?  If you find this question difficult,
>>>>>>>> please ask for some help in understanding it.
>>>>>>>
>>>>>>> Ĥ.qx(⟨Ĥ⟩, ⟨Ĥ⟩) transitions to Ĥ.qn
>>>>>>
>>>>>> An answer.  Thank you.
>>>>>>
>>>>>>      Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>>>>>
>>>>>> For Ĥ to be "exactly and precisely as in Linz" this, then, is the
>>>>>> clause
>>>>>> that applies to your H and Ĥ:
>>>>>
>>>>> There is no H in the relevant last paragraph of the Linz proof that
>>>>> forms the basis for the Linz conclusion.
>>>> Distraction.  Everything you ignore below is about the proof and refers
>>>> only to Ĥ.
>>>>
>>>>>>>>>>>>>>>>> Ĥ.q0 wM ⊢* Ĥ.qx wM wM ⊢* Ĥ.qn
>>>>>>>>>>>>>>>>> if M applied to wM does not halt
>>>>>>
>>>>>> so Ĥ (M) applied to ⟨Ĥ⟩ (wM) does not halt, but you have just told me
>>>>>> that it does.  That is what this full (but abbreviated) state
>>>>>> transition
>>>>>> sequence means:
>>>>>>
>>>>>>      Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>>>>>
>>>>>> Which is it?
>>>>>
>>>>> Ĥ0.q0 copies its input ⟨Ĥ1⟩ to ⟨Ĥ2⟩ then Ĥ0.qx simulates Ĥ1 with the
>>>>> ⟨Ĥ2⟩ copy then
>>>>> Ĥ1.q0 copies its input ⟨Ĥ2⟩ to ⟨Ĥ3⟩ then Ĥ1.qx simulates Ĥ2 with the
>>>>> ⟨Ĥ3⟩ copy then
>>>>> Ĥ2.q0 copies its input ⟨Ĥ3⟩ to ⟨Ĥ4⟩ then Ĥ2.qx simulates Ĥ3 with the
>>>>> ⟨Ĥ4⟩ copy then ...
>>>> This is an abuse of the notation (but I know what you mean).  There is
>>>> no Ĥ1 or Ĥ2.  If you think it helps to show which copy of ⟨Ĥ⟩ your
>>>> simulating "decider" is either running and/or currently looking at, you
>>>> need to come up with a notation that does that.
>>>
>>> A better notation is what I have in my PDF actual subscripts but
>>> people here tel me that their newsreader makes sure to totally ignore
>>> posts with HTML so that do even see the post at all.
>>
>> I am happy you have a notation you like.  Are you prepared to address
>> that fact that your H^ is not "as in Linz"?
>>
>
> My Ĥ is exactly the Linz Ĥ with the additional elaboration that the
> second wildcard state transition ⊢* is defined to be a simulating halt
> decider. The Linz ⊢* explicitly allows for this without diverging from
> the Linz template at all.
>
> Ĥ.q0 wM ⊢* Ĥ.qx wM wM ⊢*
>
>
>>>> At least I know what
>>>> this "math poem" means, because you've been saying this "it's a
>>>> simulator until" stuff for years.
>>>>
>>>>> The outermost Ĥ0.qx correctly decides that its input: (⟨Ĥ1⟩, ⟨Ĥ2⟩)
>>>>> can't possibly ever reach its final state. Then it transitions to
>>>>> Ĥ0.qn causing the outermost Ĥ0 to halt.
>>>> Apart from the bad notation, yes.  All those copies and tests and
>>>> eventual deciding are neatly summed up in the last ⊢* Ĥ.qn of
>>>>     Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>>>
>>>>> Because the outermost Ĥ0.qx did not decide that Ĥ0 would never halt
>>>>> and it is self evident that its input: (⟨Ĥ1⟩, ⟨Ĥ2⟩) can't possibly
>>>>> ever reach its final state there is no contradiction or paradox and it
>>>>> decided correctly.
>>>> You are free to define "decide correctly" in any way you like provided
>>>> you are honest about it.  But you hooked people in by saying that
>>>> your Ĥ
>>>> is "exactly and precisely as in Linz", and you quoted, even now, what
>>>> Linz has to say about such TMs:
>>>>     Ĥ.q0 wM ⊢* Ĥ.qx wM wM ⊢* Ĥ.qn
>>>>     if M applied to wM does not halt
>>>> This is your quote.  You brought it up.  You claimed your Ĥ was as Linz
>>>> states -- that Ĥ.q0 wM ⊢* Ĥ.qn if and only if M applied to wM does not
>>>> halt.  Linz makes no exceptions based on why the transitions from Ĥ.q0
>>>> wM to Ĥ.qn occur.  Linz does not say
>>>>     Ĥ.q0 wM ⊢* Ĥ.qx wM wM ⊢* Ĥ.qn
>>>>     if M applied to wM does not halt or if M applied wM only halts
>>>>     because...
>>>> Are you now saying that your TM was not "as in Linz"?  (You should,
>>>> because you've admitted that elsewhere.)
>>>
>>> Ĥ[0] is to be interpreted to mean Ĥ<sub>0</sub>
>>>   [0] Means the actual Turing machine and not a TM description.
>>>   [1] Means the first TM description parameter
>>>   [2] Means a copy of the the first TM description parameter
>>>
>>> Now I am saying that when the actual unmodified Linz Ĥ is understood
>>> to have a UTM/Halt-Decider at Ĥ[0].qx that this Ĥ[0].qx does correctly
>>> decide that its input: (⟨Ĥ[1]⟩, ⟨Ĥ[2]⟩) can't possibly ever reach its
>>> final state of Ĥ[1].qn or Ĥ[2].qn, therefore we know that its input
>>> never halts therefore we know that a state transition from Ĥ[0].qx to
>>> Ĥ0.qn is necessarily correct.
>>
>> We all know you are declaring that to be correct.  Here's why your Ĥ is
>> not "as in Linz".  Linz requires that
>>
>>    Ĥ.q0 wM ⊢* Ĥ.qx wM wM ⊢* Ĥ.qn
>>    if M applied to wM does not halt
>>
>> Any Ĥ that eventually transitions to Ĥ.qn on input wM must do so
>> if, and only if, the encoded M applied to wM does not halt.  But you've
>> given us a case where your Ĥ is not like this:
>>
>>    Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>
>
> And when we eliminate the fallacy of equivocation error we have
>
> Ĥ[0].q0 ⟨Ĥ⟩ ⊢* Ĥ[0].qx ⟨Ĥ[1]⟩ ⟨Ĥ[2]⟩ ⊢* Ĥ[0].qn
>
> The way that you do it when your twin bother commits a crime that makes
> you guilty.

But if you do exactly the same thing that your 'twim brother' does, like
Turing Machines do, if your 'twin brother' commits a crime, you did
exactly the same thing.

This may not be applicable for volitional people, but if one copy of
Turing Machine P is given input I and Halts or doesn't, another copy of
that exact same WILL do exactly the same thing.

>
> Ĥ[0].q0 ⟨Ĥ[1]⟩ only halts because the simulation of the
> the input to Ĥ[0].qx ⟨Ĥ[1]⟩ ⟨Ĥ[2]⟩ was aborted.
>
> (a) The simulation of the input to Ĥ[0].qx ⟨Ĥ[1]⟩ ⟨Ĥ[2]⟩
> was aborted because neither ⟨Ĥ[1]⟩ nor ⟨Ĥ[2]⟩ could
> ever possibly reach their final states.

But they WILL if allowed to execute, this is PROVEN because H^0(H^0)
does halt.

If you want to claim that H^1 behaves differently then H^0, then you did
something wrong. Either H^1 isn't the representation of H^0, or somehow
H^0 isn't a actual Turing Machine (only possible because we are working
under supposed equivalence, you can't have a ACTUAL Turing Machine that
isn't one).

But the ^ construction formula, H^ WILL be a Turing Machine as long as H
is, so if H^ isn't a Turing Machine, that requires that H is a Turing
Machine (or you have done the construction wrong). If H isn't a Turing
Machine then you failed at the intial requirements.

Maybe you don't understand that fundamental property of Turing Machines,
that ALL copies of a given machine will give the exact same reponse for
the exact same input.


Click here to read the complete article
Re: Black box halt decider is NOT a partial decider [ Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] [ succinct ]

<N9LNI.98023$VU3.62903@fx46.iad>

 copy mid

https://www.novabbs.com/devel/article-flat.php?id=19364&group=comp.theory#19364

 copy link   Newsgroups: comp.theory
Path: i2pn2.org!i2pn.org!aioe.org!news.uzoreto.com!newsfeed.xs4all.nl!newsfeed9.news.xs4all.nl!news-out.netnews.com!news.alt.net!fdc2.netnews.com!peer03.ams1!peer.ams1.xlned.com!news.xlned.com!peer01.iad!feed-me.highwinds-media.com!news.highwinds-media.com!fx46.iad.POSTED!not-for-mail
Subject: Re:_Black_box_halt_decider_is_NOT_a_partial_decider_[
Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] [ succinct
]
Newsgroups: comp.theory
References: <20210719214640.00000dfc@reddwarf.jmc>
<Ob2dneXfOsPHVGD9nZ2dnUU78aHNnZ2d@brightview.co.uk>
<tOudnQr4N_JfUGD9nZ2dnUU78fHNnZ2d@brightview.co.uk>
<877dhec8wh.fsf@bsb.me.uk> <dtudnULpgO1VVWP9nZ2dnUU7-TmdnZ2d@giganews.com>
<87pmv4ab6r.fsf@bsb.me.uk> <JNadnQD-Ofr-SJz8nZ2dnUU7-XHNnZ2d@giganews.com>
<871r7i6n2u.fsf@bsb.me.uk> <OqKdnROLKJ9CdJz8nZ2dnUU7-avNnZ2d@giganews.com>
<87k0la542c.fsf@bsb.me.uk> <1NidnVPZ-NHDl5_8nZ2dnUU7-enNnZ2d@giganews.com>
<87sfzw3ao1.fsf@bsb.me.uk> <7oKdnTjx4IC20p78nZ2dnUU7-TvNnZ2d@giganews.com>
<875yws36vt.fsf@bsb.me.uk> <j66dnbdHrpV8_p78nZ2dnUU7-aXNnZ2d@giganews.com>
<87im0s0ydp.fsf@bsb.me.uk> <Brqdnfehrf0Kj5n8nZ2dnUU7-X3NnZ2d@giganews.com>
<87tukblgjy.fsf@bsb.me.uk> <qtGdnfuXs4nFOZn8nZ2dnUU7-cnNnZ2d@giganews.com>
<871r7ekugt.fsf@bsb.me.uk> <K5-dndGZo_-VmJv8nZ2dnUU78QvNnZ2d@giganews.com>
<87czqxa0zk.fsf@bsb.me.uk> <ktidnbuI6J5g8Zr8nZ2dnUU7-XfNnZ2d@giganews.com>
From: Rich...@Damon-Family.org (Richard Damon)
User-Agent: Mozilla/5.0 (Macintosh; Intel Mac OS X 10.15; rv:78.0)
Gecko/20100101 Thunderbird/78.12.0
MIME-Version: 1.0
In-Reply-To: <ktidnbuI6J5g8Zr8nZ2dnUU7-XfNnZ2d@giganews.com>
Content-Type: text/plain; charset=utf-8
Content-Language: en-US
Content-Transfer-Encoding: 8bit
Lines: 169
Message-ID: <N9LNI.98023$VU3.62903@fx46.iad>
X-Complaints-To: abuse@easynews.com
Organization: Forte - www.forteinc.com
X-Complaints-Info: Please be sure to forward a copy of ALL headers otherwise we will be unable to process your complaint properly.
Date: Sun, 1 Aug 2021 22:13:16 -0700
X-Received-Bytes: 9311
 by: Richard Damon - Mon, 2 Aug 2021 05:13 UTC

On 8/1/21 8:56 PM, olcott wrote:
> On 8/1/2021 5:54 AM, Ben Bacarisse wrote:
>> olcott <NoOne@NoWhere.com> writes:
>>
>>> On 7/31/2021 5:08 PM, Ben Bacarisse wrote:
>>>> olcott <NoOne@NoWhere.com> writes:
>>>>
>>>>> On 7/30/2021 2:58 PM, Ben Bacarisse wrote:
>>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>>
>>>>>>> On 7/30/2021 7:39 AM, Ben Bacarisse wrote:
>>>>>>
>>>>>>>> Any chance you will now say if
>>>>>>>>
>>>>>>>>>      Ĥ.qx(⟨Ĥ⟩, ⟨Ĥ⟩)
>>>>>>>>
>>>>>>>> transitions to Ĥ.qn or Ĥ.qy?  If you find this question difficult,
>>>>>>>> please ask for some help in understanding it.
>>>>>>>
>>>>>>> Ĥ.qx(⟨Ĥ⟩, ⟨Ĥ⟩) transitions to Ĥ.qn
>>>>>>
>>>>>> An answer.  Thank you.
>>>>>>
>>>>>>      Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>>>>>
>>>>>> For Ĥ to be "exactly and precisely as in Linz" this, then, is the
>>>>>> clause
>>>>>> that applies to your H and Ĥ:
>>>>>
>>>>> There is no H in the relevant last paragraph of the Linz proof that
>>>>> forms the basis for the Linz conclusion.
>>>> Distraction.  Everything you ignore below is about the proof and refers
>>>> only to Ĥ.
>>>>
>>>>>>>>>>>>>>>>> Ĥ.q0 wM ⊢* Ĥ.qx wM wM ⊢* Ĥ.qn
>>>>>>>>>>>>>>>>> if M applied to wM does not halt
>>>>>>
>>>>>> so Ĥ (M) applied to ⟨Ĥ⟩ (wM) does not halt, but you have just told me
>>>>>> that it does.  That is what this full (but abbreviated) state
>>>>>> transition
>>>>>> sequence means:
>>>>>>
>>>>>>      Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>>>>>
>>>>>> Which is it?
>>>>>
>>>>> Ĥ0.q0 copies its input ⟨Ĥ1⟩ to ⟨Ĥ2⟩ then Ĥ0.qx simulates Ĥ1 with the
>>>>> ⟨Ĥ2⟩ copy then
>>>>> Ĥ1.q0 copies its input ⟨Ĥ2⟩ to ⟨Ĥ3⟩ then Ĥ1.qx simulates Ĥ2 with the
>>>>> ⟨Ĥ3⟩ copy then
>>>>> Ĥ2.q0 copies its input ⟨Ĥ3⟩ to ⟨Ĥ4⟩ then Ĥ2.qx simulates Ĥ3 with the
>>>>> ⟨Ĥ4⟩ copy then ...
>>>> This is an abuse of the notation (but I know what you mean).  There is
>>>> no Ĥ1 or Ĥ2.  If you think it helps to show which copy of ⟨Ĥ⟩ your
>>>> simulating "decider" is either running and/or currently looking at, you
>>>> need to come up with a notation that does that.
>>>
>>> A better notation is what I have in my PDF actual subscripts but
>>> people here tel me that their newsreader makes sure to totally ignore
>>> posts with HTML so that do even see the post at all.
>>
>> I am happy you have a notation you like.  Are you prepared to address
>> that fact that your H^ is not "as in Linz"?
>>
>>>> At least I know what
>>>> this "math poem" means, because you've been saying this "it's a
>>>> simulator until" stuff for years.
>>>>
>>>>> The outermost Ĥ0.qx correctly decides that its input: (⟨Ĥ1⟩, ⟨Ĥ2⟩)
>>>>> can't possibly ever reach its final state. Then it transitions to
>>>>> Ĥ0.qn causing the outermost Ĥ0 to halt.
>>>> Apart from the bad notation, yes.  All those copies and tests and
>>>> eventual deciding are neatly summed up in the last ⊢* Ĥ.qn of
>>>>     Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>>>
>>>>> Because the outermost Ĥ0.qx did not decide that Ĥ0 would never halt
>>>>> and it is self evident that its input: (⟨Ĥ1⟩, ⟨Ĥ2⟩) can't possibly
>>>>> ever reach its final state there is no contradiction or paradox and it
>>>>> decided correctly.
>>>> You are free to define "decide correctly" in any way you like provided
>>>> you are honest about it.  But you hooked people in by saying that
>>>> your Ĥ
>>>> is "exactly and precisely as in Linz", and you quoted, even now, what
>>>> Linz has to say about such TMs:
>>>>     Ĥ.q0 wM ⊢* Ĥ.qx wM wM ⊢* Ĥ.qn
>>>>     if M applied to wM does not halt
>>>> This is your quote.  You brought it up.  You claimed your Ĥ was as Linz
>>>> states -- that Ĥ.q0 wM ⊢* Ĥ.qn if and only if M applied to wM does not
>>>> halt.  Linz makes no exceptions based on why the transitions from Ĥ.q0
>>>> wM to Ĥ.qn occur.  Linz does not say
>>>>     Ĥ.q0 wM ⊢* Ĥ.qx wM wM ⊢* Ĥ.qn
>>>>     if M applied to wM does not halt or if M applied wM only halts
>>>>     because...
>>>> Are you now saying that your TM was not "as in Linz"?  (You should,
>>>> because you've admitted that elsewhere.)
>>>
>>> Ĥ[0] is to be interpreted to mean Ĥ<sub>0</sub>
>>>   [0] Means the actual Turing machine and not a TM description.
>>>   [1] Means the first TM description parameter
>>>   [2] Means a copy of the the first TM description parameter
>>>
>>> Now I am saying that when the actual unmodified Linz Ĥ is understood
>>> to have a UTM/Halt-Decider at Ĥ[0].qx that this Ĥ[0].qx does correctly
>>> decide that its input: (⟨Ĥ[1]⟩, ⟨Ĥ[2]⟩) can't possibly ever reach its
>>> final state of Ĥ[1].qn or Ĥ[2].qn, therefore we know that its input
>>> never halts therefore we know that a state transition from Ĥ[0].qx to
>>> Ĥ0.qn is necessarily correct.
>>
>> We all know you are declaring that to be correct.  Here's why your Ĥ is
>> not "as in Linz".  Linz requires that
>>
>>    Ĥ.q0 wM ⊢* Ĥ.qx wM wM ⊢* Ĥ.qn
>>    if M applied to wM does not halt
>>
>> Any Ĥ that eventually transitions to Ĥ.qn on input wM must do so
>> if, and only if, the encoded M applied to wM does not halt.  But you've
>> given us a case where your Ĥ is not like this:
>>
>>    Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>
> *This did not show up in my other news server so I am pointing it again*
>
> And when we eliminate the fallacy of equivocation error we have
>
> Ĥ[0].q0 ⟨Ĥ⟩ ⊢* Ĥ[0].qx ⟨Ĥ[1]⟩ ⟨Ĥ[2]⟩ ⊢* Ĥ[0].qn
>
> The way that you do it when your twin bother commits a crime that makes
> you guilty.
>
> Ĥ[0].q0 ⟨Ĥ[1]⟩ only halts because the simulation of the
> the input to Ĥ[0].qx ⟨Ĥ[1]⟩ ⟨Ĥ[2]⟩ was aborted.
>
> (a) The simulation of the input to Ĥ[0].qx ⟨Ĥ[1]⟩ ⟨Ĥ[2]⟩
> was aborted because neither ⟨Ĥ[1]⟩ nor ⟨Ĥ[2]⟩ could
> ever possibly reach their final states.
>
> (b) Because neither ⟨Ĥ[1]⟩ nor ⟨Ĥ[2]⟩ could ever possibly reach
> their final states we know that they never halt.
>
> (c) Because they never halt we know that Ĥ[0].qx correctly decided
> that its input never halts.
>
> This is the same as: X > Y & Y > Z therefore X > Z
> I do seem to have a correct chain of inference.
> I do not think that you can point to any error in
> this chain of inference.
>
> In an honest dialogue when you would disagree that a
> chain of inference derives a correct conclusion you
> would point to a specific error in this chain of inference.
>
> What is the error in (a)(b)(c) ?
>
>

See my rebuttal to your other message.

>> Here we can see that Ĥ applied to ⟨Ĥ⟩ halts.  You can call your Ĥ's
>> behaviour "correct".  You can call it anything you like.  But it's not
>> "as in Linz".  It does not say anything about Linz's proof.  It does not
>> do anything people would call impossible or even interesting.
>>
>> Presumably, you will simply explain, yet again, why you choose to call
>> it correct.  You might even, yet again, quote the symbols from Linz that
>> don't apply to your Ĥ in order to make you posts seem relevant.
>>
>
>


Click here to read the complete article
Re: Black box halt decider is NOT a partial decider [ Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] ( Are you game ? )

<87y29j6c5e.fsf@bsb.me.uk>

 copy mid

https://www.novabbs.com/devel/article-flat.php?id=19370&group=comp.theory#19370

 copy link   Newsgroups: comp.theory
Followup: comp.theory
Path: i2pn2.org!i2pn.org!eternal-september.org!reader02.eternal-september.org!.POSTED!not-for-mail
From: ben.use...@bsb.me.uk (Ben Bacarisse)
Newsgroups: comp.theory
Subject: Re: Black box halt decider is NOT a partial decider [
Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] (
Are you game ? )
Followup-To: comp.theory
Date: Mon, 02 Aug 2021 17:31:57 +0100
Organization: A noiseless patient Spider
Lines: 89
Message-ID: <87y29j6c5e.fsf@bsb.me.uk>
References: <20210719214640.00000dfc@reddwarf.jmc>
<Ob2dneXfOsPHVGD9nZ2dnUU78aHNnZ2d@brightview.co.uk>
<tOudnQr4N_JfUGD9nZ2dnUU78fHNnZ2d@brightview.co.uk>
<877dhec8wh.fsf@bsb.me.uk>
<dtudnULpgO1VVWP9nZ2dnUU7-TmdnZ2d@giganews.com>
<87pmv4ab6r.fsf@bsb.me.uk>
<JNadnQD-Ofr-SJz8nZ2dnUU7-XHNnZ2d@giganews.com>
<871r7i6n2u.fsf@bsb.me.uk>
<OqKdnROLKJ9CdJz8nZ2dnUU7-avNnZ2d@giganews.com>
<87k0la542c.fsf@bsb.me.uk>
<x5mdnTC66uNJip_8nZ2dnUU7-aWdnZ2d@giganews.com>
<87mtq438ge.fsf@bsb.me.uk>
<PbednTcmR4_Mw578nZ2dnUU78WvNnZ2d@giganews.com>
<87tukc12yh.fsf@bsb.me.uk>
<e6OdnW_rdvusk5n8nZ2dnUU7-dPNnZ2d@giganews.com>
<875ywrmwsr.fsf@bsb.me.uk>
<GtmdnfBrysPrAZn8nZ2dnUU7-L_NnZ2d@giganews.com>
<874kcakv3d.fsf@bsb.me.uk>
<-M-dnfsXl4WvWpj8nZ2dnUU7-IGdnZ2d@giganews.com>
<87im0pa1pp.fsf@bsb.me.uk>
<6eOdnaoMUdZN_pr8nZ2dnUU7-cPNnZ2d@giganews.com>
Mime-Version: 1.0
Content-Type: text/plain; charset=utf-8
Content-Transfer-Encoding: 8bit
Injection-Info: reader02.eternal-september.org; posting-host="af295d6d9f98babc0aeed64523984724";
logging-data="20487"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/y8klwnoWbzlSvIXtefqL+7pF1m+5VkEc="
Cancel-Lock: sha1:DPIrPjkLKUFH4fYMFspvFgcc3ak=
sha1:JcF0mDn6qiJYo8oUUDTlCE1dZCg=
X-BSB-Auth: 1.d22e0826799cfe133095.20210802173157BST.87y29j6c5e.fsf@bsb.me.uk
 by: Ben Bacarisse - Mon, 2 Aug 2021 16:31 UTC

olcott <NoOne@NoWhere.com> writes:

> On 8/1/2021 5:39 AM, Ben Bacarisse wrote:
>> olcott <NoOne@NoWhere.com> writes:
>>
>>> On 7/31/2021 4:54 PM, Ben Bacarisse wrote:
>>>> olcott <NoOne@NoWhere.com> writes:
>>>>
>>>>> It matters not what I had.
>>>> Because you can't justify it the honest debate you claim to want.
>>>>
>>>>> It only matters what I have.
>>>> I.e. nothing of any interest. You make it plain in a previous reply
>>>> that you've had nothing of interest going right back to the original
>>>> deceptive claim.
>>>>
>>>>> If you are sincere about an honest dialogue then we must quit focusing
>>>>> on details of obsolete technology.
>>>> And yet you skipped the big picture part:
>>>>
>>>>>> (5) You said you had "an H that decides (Ĥ, Ĥ)". What decision did your
>>>>>> Dec 2018 code come to about "(Ĥ, Ĥ)"?
>>>>>
>>>>> The 2018 version Halts(H_Hat, H_Hat)==0 in the exact same way that
>>>>> H(P,P)==0 now except that the never halting criteria is much more
>>>>> elaborate. The initial criteria was very crude.
>>>>
>>>> Ah, so you never had H and H_Hat that do anything that anyone would say
>>>> is impossible. Had you said, back in Dec 2018, "I have C code such that
>>>> H(H_Hat, H_Hat) == 0 but H_Hat(H_Hat) halts" no one would have been
>>>> interested.
>>>
>>> If you are sincere about an honest dialogue then we must quit focusing
>>> on details of obsolete technology.
>>
>> Ah, an honest dialogue requires me to ignore your past deception? Well,
>> I can accommodate that: you /currently/ don't have anything that anyone
>> would consider to be impossible or even interesting. An H/H_Hat pair
>> such that H(H_Hat, H_Hat) == 0 and H_Hat(H_Hat) halts is of no interest
>> to anyone. Is that better?
>
> When H is a simulating partial halt decider and the halt decider
> embedded in Ĥ at Ĥ.qx is a simulating halt decider then:
>
> It is the case that the input to H(P,P) and the input to Ĥ(⟨Ĥ⟩) cannot
> possibly ever reach their final state and must have their simulation
> aborted to prevent the infinite execution of P and Ĥ.
>
> Let's have an honest dialogue about that.

Yes, let's. Here's how to say what happens without all those vague
(and, frankly, incorrect) words:

Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn

If you don't mean

Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn

can you say what you do mean formally? Formally means using some
formal notation like Linz does.

If what you want to say is all about what happens in that second ⊢*
(i.e. all the nested simulations and so on) then don't bother, because
what makes your Ĥ irrelevant is what state Ĥ applied to ⟨Ĥ⟩ gets to, not
how it gets there.

>>>> I think you owe everyone an apology. Even if there was no indent to
>>>> deceive, your words back then did everything possible to suggest some
>>>> impossible Turing machine. And you wouldn't say, until recently, even
>>>> when explicitly asked, what decision H came to. It was fishy from the
>>>> start.
>> You still owe everyone an apology. Neither Turing machines nor C code
>> are obsolete technology. If you really had what you falsely claimed to
>> have had, posting it at any time in the last 30 months would have
>> settled the matter. It still would, but you either never had anything
>> at all or you are too embarrassed to post what it was.
>
> The technology that I had in 2018 is obsolete and not relevant to an
> honest dialogue about the technology that I currently have.

You had C code. C code is not obsolete. It's also a good formalism.
You could say what you meant back then by posting the code. But you
won't post it either because you never had it or you are embarrassed by
it. An honest academic would simply say "this is what I had -- very
rough and ready, isn't it? Here's the tidied up version...".

--
Ben.

Re: Black box halt decider is NOT a partial decider [ Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] ( Are you game ? )

<p8SdnV8dJu3wq5X8nZ2dnUU7-a3NnZ2d@giganews.com>

 copy mid

https://www.novabbs.com/devel/article-flat.php?id=19374&group=comp.theory#19374

 copy link   Newsgroups: comp.theory comp.ai.philosophy comp.software-eng sci.math.symbolic
Path: i2pn2.org!i2pn.org!aioe.org!news.uzoreto.com!tr2.eu1.usenetexpress.com!feeder.usenetexpress.com!tr2.iad1.usenetexpress.com!border1.nntp.dca1.giganews.com!nntp.giganews.com!buffer1.nntp.dca1.giganews.com!buffer2.nntp.dca1.giganews.com!news.giganews.com.POSTED!not-for-mail
NNTP-Posting-Date: Mon, 02 Aug 2021 13:16:13 -0500
Subject: Re:_Black_box_halt_decider_is_NOT_a_partial_decider_[ Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] ( Are you game_?_)
Newsgroups: comp.theory,comp.ai.philosophy,comp.software-eng,sci.math.symbolic
References: <20210719214640.00000dfc@reddwarf.jmc> <Ob2dneXfOsPHVGD9nZ2dnUU78aHNnZ2d@brightview.co.uk> <tOudnQr4N_JfUGD9nZ2dnUU78fHNnZ2d@brightview.co.uk> <877dhec8wh.fsf@bsb.me.uk> <dtudnULpgO1VVWP9nZ2dnUU7-TmdnZ2d@giganews.com> <87pmv4ab6r.fsf@bsb.me.uk> <JNadnQD-Ofr-SJz8nZ2dnUU7-XHNnZ2d@giganews.com> <871r7i6n2u.fsf@bsb.me.uk> <OqKdnROLKJ9CdJz8nZ2dnUU7-avNnZ2d@giganews.com> <87k0la542c.fsf@bsb.me.uk> <x5mdnTC66uNJip_8nZ2dnUU7-aWdnZ2d@giganews.com> <87mtq438ge.fsf@bsb.me.uk> <PbednTcmR4_Mw578nZ2dnUU78WvNnZ2d@giganews.com> <87tukc12yh.fsf@bsb.me.uk> <e6OdnW_rdvusk5n8nZ2dnUU7-dPNnZ2d@giganews.com> <875ywrmwsr.fsf@bsb.me.uk> <GtmdnfBrysPrAZn8nZ2dnUU7-L_NnZ2d@giganews.com> <874kcakv3d.fsf@bsb.me.uk> <-M-dnfsXl4WvWpj8nZ2dnUU7-IGdnZ2d@giganews.com> <87im0pa1pp.fsf@bsb.me.uk> <6eOdnaoMUdZN_pr8nZ2dnUU7-cPNnZ2d@giganews.com> <87y29j6c5e.fsf@bsb.me.uk>
From: NoO...@NoWhere.com (olcott)
Date: Mon, 2 Aug 2021 13:16:12 -0500
User-Agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64; rv:78.0) Gecko/20100101 Thunderbird/78.12.0
MIME-Version: 1.0
In-Reply-To: <87y29j6c5e.fsf@bsb.me.uk>
Content-Type: text/plain; charset=utf-8; format=flowed
Content-Language: en-US
Content-Transfer-Encoding: 8bit
Message-ID: <p8SdnV8dJu3wq5X8nZ2dnUU7-a3NnZ2d@giganews.com>
Lines: 112
X-Usenet-Provider: http://www.giganews.com
X-Trace: sv3-iYuV0xqbyWPsLppt8/BYUhLvrZ6WAyifEcJMdsXjj6s2MVTHnJzm2SaDlA1976Xj2fAF7GU6qKNLOz3!+3ldaYce7WdFGs2rT/ozWrBJYejZAGvXFrO061Fv215EnqH75eGsRjawgxeoqqN8jIYKhkGQeQ==
X-Complaints-To: abuse@giganews.com
X-DMCA-Notifications: http://www.giganews.com/info/dmca.html
X-Abuse-and-DMCA-Info: Please be sure to forward a copy of ALL headers
X-Abuse-and-DMCA-Info: Otherwise we will be unable to process your complaint properly
X-Postfilter: 1.3.40
X-Original-Bytes: 7194
 by: olcott - Mon, 2 Aug 2021 18:16 UTC

On 8/2/2021 11:31 AM, Ben Bacarisse wrote:
> olcott <NoOne@NoWhere.com> writes:
>
>> On 8/1/2021 5:39 AM, Ben Bacarisse wrote:
>>> olcott <NoOne@NoWhere.com> writes:
>>>
>>>> On 7/31/2021 4:54 PM, Ben Bacarisse wrote:
>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>
>>>>>> It matters not what I had.
>>>>> Because you can't justify it the honest debate you claim to want.
>>>>>
>>>>>> It only matters what I have.
>>>>> I.e. nothing of any interest. You make it plain in a previous reply
>>>>> that you've had nothing of interest going right back to the original
>>>>> deceptive claim.
>>>>>
>>>>>> If you are sincere about an honest dialogue then we must quit focusing
>>>>>> on details of obsolete technology.
>>>>> And yet you skipped the big picture part:
>>>>>
>>>>>>> (5) You said you had "an H that decides (Ĥ, Ĥ)". What decision did your
>>>>>>> Dec 2018 code come to about "(Ĥ, Ĥ)"?
>>>>>>
>>>>>> The 2018 version Halts(H_Hat, H_Hat)==0 in the exact same way that
>>>>>> H(P,P)==0 now except that the never halting criteria is much more
>>>>>> elaborate. The initial criteria was very crude.
>>>>>
>>>>> Ah, so you never had H and H_Hat that do anything that anyone would say
>>>>> is impossible. Had you said, back in Dec 2018, "I have C code such that
>>>>> H(H_Hat, H_Hat) == 0 but H_Hat(H_Hat) halts" no one would have been
>>>>> interested.
>>>>
>>>> If you are sincere about an honest dialogue then we must quit focusing
>>>> on details of obsolete technology.
>>>
>>> Ah, an honest dialogue requires me to ignore your past deception? Well,
>>> I can accommodate that: you /currently/ don't have anything that anyone
>>> would consider to be impossible or even interesting. An H/H_Hat pair
>>> such that H(H_Hat, H_Hat) == 0 and H_Hat(H_Hat) halts is of no interest
>>> to anyone. Is that better?
>>
>> When H is a simulating partial halt decider and the halt decider
>> embedded in Ĥ at Ĥ.qx is a simulating halt decider then:
>>
>> It is the case that the input to H(P,P) and the input to Ĥ(⟨Ĥ⟩) cannot
>> possibly ever reach their final state and must have their simulation
>> aborted to prevent the infinite execution of P and Ĥ.
>>
>> Let's have an honest dialogue about that.
>
> Yes, let's. Here's how to say what happens without all those vague
> (and, frankly, incorrect) words:
>
> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>
> If you don't mean
>
> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>
> can you say what you do mean formally? Formally means using some
> formal notation like Linz does.
>

As Linz already specifies yet does not encode in his notation there are
at least three separate and distinct instances of Ĥ.

The first one of these instances is the actual Turing machine Ĥ.
The second one is the TM description ⟨Ĥ⟩ input to Ĥ.
The third one is the copy of the TM description ⟨Ĥ⟩ input to Ĥ.

If we do not keep track of these distinctions then it seems like Ĥ.qx
decides that its input never halts and then its input immediately halts.
This would be an actual contradiction.

When we do keep track of these distinctions then the input: ⟨Ĥ^1⟩ to Ĥ^0
can be understood to never reach its final states Ĥ^1.qy or Ĥ^1.qn thus
proving that Ĥ^0.qx did correctly decide that its input ⟨Ĥ^1⟩ ⟨Ĥ^2⟩
never halts.

> If what you want to say is all about what happens in that second ⊢*
> (i.e. all the nested simulations and so on) then don't bother, because
> what makes your Ĥ irrelevant is what state Ĥ applied to ⟨Ĥ⟩ gets to, not
> how it gets there.
>
>>>>> I think you owe everyone an apology. Even if there was no indent to
>>>>> deceive, your words back then did everything possible to suggest some
>>>>> impossible Turing machine. And you wouldn't say, until recently, even
>>>>> when explicitly asked, what decision H came to. It was fishy from the
>>>>> start.
>>> You still owe everyone an apology. Neither Turing machines nor C code
>>> are obsolete technology. If you really had what you falsely claimed to
>>> have had, posting it at any time in the last 30 months would have
>>> settled the matter. It still would, but you either never had anything
>>> at all or you are too embarrassed to post what it was.
>>
>> The technology that I had in 2018 is obsolete and not relevant to an
>> honest dialogue about the technology that I currently have.
>
> You had C code. C code is not obsolete. It's also a good formalism.
> You could say what you meant back then by posting the code. But you
> won't post it either because you never had it or you are embarrassed by
> it. An honest academic would simply say "this is what I had -- very
> rough and ready, isn't it? Here's the tidied up version...".
>

--
Copyright 2021 Pete Olcott

"Great spirits have always encountered violent opposition from mediocre
minds." Einstein

Re: Black box halt decider is NOT a partial decider [ Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] ( Are you game ? )

<DYednaixofwWpZX8nZ2dnUU78eHNnZ2d@giganews.com>

 copy mid

https://www.novabbs.com/devel/article-flat.php?id=19375&group=comp.theory#19375

 copy link   Newsgroups: comp.theory comp.ai.philosophy comp.software-eng sci.math.symbolic
Path: i2pn2.org!i2pn.org!weretis.net!feeder8.news.weretis.net!border2.nntp.ams1.giganews.com!nntp.giganews.com!buffer2.nntp.ams1.giganews.com!buffer1.nntp.ams1.giganews.com!news.giganews.com.POSTED!not-for-mail
NNTP-Posting-Date: Mon, 02 Aug 2021 13:25:14 -0500
Subject: Re:_Black_box_halt_decider_is_NOT_a_partial_decider_[
Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] ( Are you g
ame_?_)
Newsgroups: comp.theory,comp.ai.philosophy,comp.software-eng,sci.math.symbolic
References: <20210719214640.00000dfc@reddwarf.jmc>
<Ob2dneXfOsPHVGD9nZ2dnUU78aHNnZ2d@brightview.co.uk>
<tOudnQr4N_JfUGD9nZ2dnUU78fHNnZ2d@brightview.co.uk>
<877dhec8wh.fsf@bsb.me.uk> <dtudnULpgO1VVWP9nZ2dnUU7-TmdnZ2d@giganews.com>
<87pmv4ab6r.fsf@bsb.me.uk> <JNadnQD-Ofr-SJz8nZ2dnUU7-XHNnZ2d@giganews.com>
<871r7i6n2u.fsf@bsb.me.uk> <OqKdnROLKJ9CdJz8nZ2dnUU7-avNnZ2d@giganews.com>
<87k0la542c.fsf@bsb.me.uk> <x5mdnTC66uNJip_8nZ2dnUU7-aWdnZ2d@giganews.com>
<87mtq438ge.fsf@bsb.me.uk> <PbednTcmR4_Mw578nZ2dnUU78WvNnZ2d@giganews.com>
<87tukc12yh.fsf@bsb.me.uk> <e6OdnW_rdvusk5n8nZ2dnUU7-dPNnZ2d@giganews.com>
<875ywrmwsr.fsf@bsb.me.uk> <GtmdnfBrysPrAZn8nZ2dnUU7-L_NnZ2d@giganews.com>
<874kcakv3d.fsf@bsb.me.uk> <-M-dnfsXl4WvWpj8nZ2dnUU7-IGdnZ2d@giganews.com>
<87im0pa1pp.fsf@bsb.me.uk> <6eOdnaoMUdZN_pr8nZ2dnUU7-cPNnZ2d@giganews.com>
<87y29j6c5e.fsf@bsb.me.uk> <p8SdnV8dJu3wq5X8nZ2dnUU7-a3NnZ2d@giganews.com>
From: NoO...@NoWhere.com (olcott)
Date: Mon, 2 Aug 2021 13:25:13 -0500
User-Agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64; rv:78.0) Gecko/20100101
Thunderbird/78.12.0
MIME-Version: 1.0
In-Reply-To: <p8SdnV8dJu3wq5X8nZ2dnUU7-a3NnZ2d@giganews.com>
Content-Type: text/plain; charset=utf-8; format=flowed
Content-Language: en-US
Content-Transfer-Encoding: 8bit
Message-ID: <DYednaixofwWpZX8nZ2dnUU78eHNnZ2d@giganews.com>
Lines: 130
X-Usenet-Provider: http://www.giganews.com
X-Trace: sv3-eiCNN5SdcYvoYje3kennjNcl+2E56TMXhgb0m3dGo6l19UnYU8b9czwvuJR173AvXykx2+I+yaMFMuD!SEky/mW33bd6HocUyWrHzM8fEvWLow1wWG8UoiagsnKzg079m7oGYmaTMS82edCbR9Vp3qHioA==
X-Complaints-To: abuse@giganews.com
X-DMCA-Notifications: http://www.giganews.com/info/dmca.html
X-Abuse-and-DMCA-Info: Please be sure to forward a copy of ALL headers
X-Abuse-and-DMCA-Info: Otherwise we will be unable to process your complaint properly
X-Postfilter: 1.3.40
X-Original-Bytes: 7801
 by: olcott - Mon, 2 Aug 2021 18:25 UTC

On 8/2/2021 1:16 PM, olcott wrote:
> On 8/2/2021 11:31 AM, Ben Bacarisse wrote:
>> olcott <NoOne@NoWhere.com> writes:
>>
>>> On 8/1/2021 5:39 AM, Ben Bacarisse wrote:
>>>> olcott <NoOne@NoWhere.com> writes:
>>>>
>>>>> On 7/31/2021 4:54 PM, Ben Bacarisse wrote:
>>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>>
>>>>>>> It matters not what I had.
>>>>>> Because you can't justify it the honest debate you claim to want.
>>>>>>
>>>>>>> It only matters what I have.
>>>>>> I.e. nothing of any interest.  You make it plain in a previous reply
>>>>>> that you've had nothing of interest going right back to the original
>>>>>> deceptive claim.
>>>>>>
>>>>>>> If you are sincere about an honest dialogue then we must quit
>>>>>>> focusing
>>>>>>> on details of obsolete technology.
>>>>>> And yet you skipped the big picture part:
>>>>>>
>>>>>>>> (5) You said you had "an H that decides (Ĥ, Ĥ)".  What decision
>>>>>>>> did your
>>>>>>>>        Dec 2018 code come to about "(Ĥ, Ĥ)"?
>>>>>>>
>>>>>>> The 2018 version Halts(H_Hat, H_Hat)==0 in the exact same way that
>>>>>>> H(P,P)==0 now except that the never halting criteria is much more
>>>>>>> elaborate. The initial criteria was very crude.
>>>>>>
>>>>>> Ah, so you never had H and H_Hat that do anything that anyone
>>>>>> would say
>>>>>> is impossible.  Had you said, back in Dec 2018, "I have C code
>>>>>> such that
>>>>>> H(H_Hat, H_Hat) == 0 but H_Hat(H_Hat) halts" no one would have been
>>>>>> interested.
>>>>>
>>>>> If you are sincere about an honest dialogue then we must quit focusing
>>>>> on details of obsolete technology.
>>>>
>>>> Ah, an honest dialogue requires me to ignore your past deception?
>>>> Well,
>>>> I can accommodate that: you /currently/ don't have anything that anyone
>>>> would consider to be impossible or even interesting.  An H/H_Hat pair
>>>> such that H(H_Hat, H_Hat) == 0 and H_Hat(H_Hat) halts is of no interest
>>>> to anyone.  Is that better?
>>>
>>> When H is a simulating partial halt decider and the halt decider
>>> embedded in Ĥ at Ĥ.qx is a simulating halt decider then:
>>>
>>> It is the case that the input to H(P,P) and the input to Ĥ(⟨Ĥ⟩) cannot
>>> possibly ever reach their final state and must have their simulation
>>> aborted to prevent the infinite execution of P and Ĥ.
>>>
>>> Let's have an honest dialogue about that.
>>
>> Yes, let's.  Here's how to say what happens without all those vague
>> (and, frankly, incorrect) words:
>>
>>    Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>
>> If you don't mean
>>
>>    Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>
>> can you say what you do mean formally?  Formally means using some
>> formal notation like Linz does.
>>
>
> As Linz already specifies yet does not encode in his notation there are
> at least three separate and distinct instances of Ĥ.
>
> The first one of these instances is the actual Turing machine Ĥ.
> The second one is the TM description ⟨Ĥ⟩ input to Ĥ.
> The third one is the copy of the TM description ⟨Ĥ⟩ input to Ĥ.
>
> If we do not keep track of these distinctions then it seems like Ĥ.qx
> decides that its input never halts and then its input immediately halts.
> This would be an actual contradiction.
>
> When we do keep track of these distinctions then the input: ⟨Ĥ^1⟩ to Ĥ^0
> can be understood to never reach its final states Ĥ^1.qy or Ĥ^1.qn thus
> proving that Ĥ^0.qx did correctly decide that its input ⟨Ĥ^1⟩ ⟨Ĥ^2⟩
> never halts.

H[0] means H<sub>0</sub>

When we do keep track of these distinctions then the input: ⟨Ĥ[1]⟩ to
Ĥ[0] can be understood to never reach its final states Ĥ[1].qy or
Ĥ[1].qn thus proving that Ĥ[0].qx did correctly decide that its input
⟨Ĥ[1]⟩ ⟨Ĥ[2]⟩ never halts.

>> If what you want to say is all about what happens in that second ⊢*
>> (i.e. all the nested simulations and so on) then don't bother, because
>> what makes your Ĥ irrelevant is what state Ĥ applied to ⟨Ĥ⟩ gets to, not
>> how it gets there.
>>
>>>>>> I think you owe everyone an apology.  Even if there was no indent to
>>>>>> deceive, your words back then did everything possible to suggest some
>>>>>> impossible Turing machine.  And you wouldn't say, until recently,
>>>>>> even
>>>>>> when explicitly asked, what decision H came to.  It was fishy from
>>>>>> the
>>>>>> start.
>>>> You still owe everyone an apology.  Neither Turing machines nor C code
>>>> are obsolete technology.  If you really had what you falsely claimed to
>>>> have had, posting it at any time in the last 30 months would have
>>>> settled the matter.  It still would, but you either never had anything
>>>> at all or you are too embarrassed to post what it was.
>>>
>>> The technology that I had in 2018 is obsolete and not relevant to an
>>> honest dialogue about the technology that I currently have.
>>
>> You had C code.  C code is not obsolete.  It's also a good formalism.
>> You could say what you meant back then by posting the code.  But you
>> won't post it either because you never had it or you are embarrassed by
>> it.  An honest academic would simply say "this is what I had -- very
>> rough and ready, isn't it?  Here's the tidied up version...".
>>
>
>

--
Copyright 2021 Pete Olcott

"Great spirits have always encountered violent opposition from mediocre
minds." Einstein

Re: Black box halt decider is NOT a partial decider [ Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] [ succinct ]

<87mtpz64sq.fsf@bsb.me.uk>

 copy mid

https://www.novabbs.com/devel/article-flat.php?id=19377&group=comp.theory#19377

 copy link   Newsgroups: comp.theory
Followup: comp.theory
Path: i2pn2.org!i2pn.org!eternal-september.org!reader02.eternal-september.org!.POSTED!not-for-mail
From: ben.use...@bsb.me.uk (Ben Bacarisse)
Newsgroups: comp.theory
Subject: Re: Black box halt decider is NOT a partial decider [
Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] [
succinct ]
Followup-To: comp.theory
Date: Mon, 02 Aug 2021 20:10:45 +0100
Organization: A noiseless patient Spider
Lines: 90
Message-ID: <87mtpz64sq.fsf@bsb.me.uk>
References: <20210719214640.00000dfc@reddwarf.jmc> <877dhec8wh.fsf@bsb.me.uk>
<dtudnULpgO1VVWP9nZ2dnUU7-TmdnZ2d@giganews.com>
<87pmv4ab6r.fsf@bsb.me.uk>
<JNadnQD-Ofr-SJz8nZ2dnUU7-XHNnZ2d@giganews.com>
<871r7i6n2u.fsf@bsb.me.uk>
<OqKdnROLKJ9CdJz8nZ2dnUU7-avNnZ2d@giganews.com>
<87k0la542c.fsf@bsb.me.uk>
<1NidnVPZ-NHDl5_8nZ2dnUU7-enNnZ2d@giganews.com>
<87sfzw3ao1.fsf@bsb.me.uk>
<7oKdnTjx4IC20p78nZ2dnUU7-TvNnZ2d@giganews.com>
<875yws36vt.fsf@bsb.me.uk>
<j66dnbdHrpV8_p78nZ2dnUU7-aXNnZ2d@giganews.com>
<87im0s0ydp.fsf@bsb.me.uk>
<Brqdnfehrf0Kj5n8nZ2dnUU7-X3NnZ2d@giganews.com>
<87tukblgjy.fsf@bsb.me.uk>
<qtGdnfuXs4nFOZn8nZ2dnUU7-cnNnZ2d@giganews.com>
<871r7ekugt.fsf@bsb.me.uk>
<K5-dndGZo_-VmJv8nZ2dnUU78QvNnZ2d@giganews.com>
<87czqxa0zk.fsf@bsb.me.uk>
<woudnXWBxPba95r8nZ2dnUU78ffNnZ2d@giganews.com>
Mime-Version: 1.0
Content-Type: text/plain; charset=utf-8
Content-Transfer-Encoding: 8bit
Injection-Info: reader02.eternal-september.org; posting-host="af295d6d9f98babc0aeed64523984724";
logging-data="24175"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1+ZqhDoy32DZezJem4jVtQ/341G/aIs2Fk="
Cancel-Lock: sha1:U671iyYdb5X/Hex+STcbYuhXTcc=
sha1:/bLWwc7jwDjjtgHp406NhAv5Xhw=
X-BSB-Auth: 1.e63685e54b46b82fb3f9.20210802201045BST.87mtpz64sq.fsf@bsb.me.uk
 by: Ben Bacarisse - Mon, 2 Aug 2021 19:10 UTC

olcott <NoOne@NoWhere.com> writes:

> On 8/1/2021 5:54 AM, Ben Bacarisse wrote:

>> I am happy you have a notation you like. Are you prepared to address
>> that fact that your H^ is not "as in Linz"?
>
> My Ĥ is exactly the Linz Ĥ with the additional elaboration that the
> second wildcard state transition ⊢* is defined to be a simulating halt
> decider.

No. I've explained many times now why your Ĥ is not at all "the Linz
Ĥ". Do you see any point in my doing so again?

>> We all know you are declaring that to be correct. Here's why your Ĥ is
>> not "as in Linz". Linz requires that
>>
>> Ĥ.q0 wM ⊢* Ĥ.qx wM wM ⊢* Ĥ.qn
>> if M applied to wM does not halt
>>
>> Any Ĥ that eventually transitions to Ĥ.qn on input wM must do so
>> if, and only if, the encoded M applied to wM does not halt. But you've
>> given us a case where your Ĥ is not like this:
>>
>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>
> And when we eliminate the fallacy of equivocation error we have
>
> Ĥ[0].q0 ⟨Ĥ⟩ ⊢* Ĥ[0].qx ⟨Ĥ[1]⟩ ⟨Ĥ[2]⟩ ⊢* Ĥ[0].qn

The only thing I think you are equivocating on is pretending that Ĥ[0]
is not Ĥ, and it doesn't look as if you've removed that error. I think
you /should/ remove it so that you can be saying something of value
about Ĥ.

> The way that you do it when your twin bother commits a crime that
> makes you guilty.
>
> Ĥ[0].q0 ⟨Ĥ[1]⟩ only halts because the simulation of the
> the input to Ĥ[0].qx ⟨Ĥ[1]⟩ ⟨Ĥ[2]⟩ was aborted.
>
> (a) The simulation of the input to Ĥ[0].qx ⟨Ĥ[1]⟩ ⟨Ĥ[2]⟩
> was aborted because neither ⟨Ĥ[1]⟩ nor ⟨Ĥ[2]⟩ could
> ever possibly reach their final states.
>
> (b) Because neither ⟨Ĥ[1]⟩ nor ⟨Ĥ[2]⟩ could ever possibly reach
> their final states we know that they never halt.
>
> (c) Because they never halt we know that Ĥ[0].qx correctly decided
> that its input never halts.
>
> This is the same as: X > Y & Y > Z therefore X > Z
> I do seem to have a correct chain of inference.
> I do not think that you can point to any error in
> this chain of inference.
>
> In an honest dialogue when you would disagree that a
> chain of inference derives a correct conclusion you
> would point to a specific error in this chain of inference.
>
> What is the error in (a)(b)(c) ?

Far too many to go into all of them (if you are not inclined to correct
anything, just jump to number 7) but ere are some:

(1) Unless Ĥ[0] is just another name for Ĥ you are not saying anything I
care about. What matters is what Ĥ applied to ⟨Ĥ⟩ does.

(2) TMs don't "abort". The sequence of configurations ends.

(3) Stop talking about what "could possibly" happen. TMs do what they
do. There are no "possibilities".

(4) ⟨Ĥ[1]⟩ and ⟨Ĥ[2]⟩ are strings. A string does not "reach" anything.
Strings don't even have states that can be reached. I can unravel
this, but why must your readers work hard to unpick your metaphors?

(5) Ĥ[0].qx is a state. It does not decide anything. (Again, I can
guess what you mean but you asked for help.)

(6) States don't have input. Whilst I could guess that you mean "the
tape" at the point the state is entered", states in a TM may be
entered many times so there is no obvious single "input".

(7) The correct behaviour of Ĥ is not based on (a) and (b) but on what
Linz says about Ĥ applied to ⟨Ĥ⟩. Your Ĥ does not behave as Linz's
Ĥ should, even in the one case you care about.

--
Ben.

Re: Black box halt decider is NOT a partial decider [ Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] [ succinct ]

<87h7g764rb.fsf@bsb.me.uk>

 copy mid

https://www.novabbs.com/devel/article-flat.php?id=19378&group=comp.theory#19378

 copy link   Newsgroups: comp.theory
Path: i2pn2.org!i2pn.org!eternal-september.org!reader02.eternal-september.org!.POSTED!not-for-mail
From: ben.use...@bsb.me.uk (Ben Bacarisse)
Newsgroups: comp.theory
Subject: Re: Black box halt decider is NOT a partial decider [
Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] [
succinct ]
Date: Mon, 02 Aug 2021 20:11:36 +0100
Organization: A noiseless patient Spider
Lines: 10
Message-ID: <87h7g764rb.fsf@bsb.me.uk>
References: <20210719214640.00000dfc@reddwarf.jmc> <877dhec8wh.fsf@bsb.me.uk>
<dtudnULpgO1VVWP9nZ2dnUU7-TmdnZ2d@giganews.com>
<87pmv4ab6r.fsf@bsb.me.uk>
<JNadnQD-Ofr-SJz8nZ2dnUU7-XHNnZ2d@giganews.com>
<871r7i6n2u.fsf@bsb.me.uk>
<OqKdnROLKJ9CdJz8nZ2dnUU7-avNnZ2d@giganews.com>
<87k0la542c.fsf@bsb.me.uk>
<1NidnVPZ-NHDl5_8nZ2dnUU7-enNnZ2d@giganews.com>
<87sfzw3ao1.fsf@bsb.me.uk>
<7oKdnTjx4IC20p78nZ2dnUU7-TvNnZ2d@giganews.com>
<875yws36vt.fsf@bsb.me.uk>
<j66dnbdHrpV8_p78nZ2dnUU7-aXNnZ2d@giganews.com>
<87im0s0ydp.fsf@bsb.me.uk>
<Brqdnfehrf0Kj5n8nZ2dnUU7-X3NnZ2d@giganews.com>
<87tukblgjy.fsf@bsb.me.uk>
<qtGdnfuXs4nFOZn8nZ2dnUU7-cnNnZ2d@giganews.com>
<871r7ekugt.fsf@bsb.me.uk>
<K5-dndGZo_-VmJv8nZ2dnUU78QvNnZ2d@giganews.com>
<87czqxa0zk.fsf@bsb.me.uk>
<ktidnbuI6J5g8Zr8nZ2dnUU7-XfNnZ2d@giganews.com>
Mime-Version: 1.0
Content-Type: text/plain
Injection-Info: reader02.eternal-september.org; posting-host="af295d6d9f98babc0aeed64523984724";
logging-data="24175"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/ulGx2f3KJIVRXANDylF/LFY0Vjbd7E88="
Cancel-Lock: sha1:tcgBP9/PJCyWMKdX9+CsxkS3ew0=
sha1:lIKUEbUEtdO94q7h9ir4pTcwxf8=
X-BSB-Auth: 1.36cc720fcabb839581c0.20210802201136BST.87h7g764rb.fsf@bsb.me.uk
 by: Ben Bacarisse - Mon, 2 Aug 2021 19:11 UTC

olcott <NoOne@NoWhere.com> writes:

> *This did not show up in my other news server so I am pointing it
> again*

It did in mine and I replied. I won't reply again. With luck you won't
see my reply.

--
Ben.

Re: Black box halt decider is NOT a partial decider [ Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] [ succinct ]

<w5edne8d06OkxpX8nZ2dnUU7-b_NnZ2d@giganews.com>

 copy mid

https://www.novabbs.com/devel/article-flat.php?id=19381&group=comp.theory#19381

 copy link   Newsgroups: comp.theory comp.ai.philosophy comp.software-eng sci.math.symbolic
Path: i2pn2.org!i2pn.org!weretis.net!feeder6.news.weretis.net!news.snarked.org!border2.nntp.dca1.giganews.com!nntp.giganews.com!buffer2.nntp.dca1.giganews.com!buffer1.nntp.dca1.giganews.com!news.giganews.com.POSTED!not-for-mail
NNTP-Posting-Date: Mon, 02 Aug 2021 15:53:13 -0500
Subject: Re:_Black_box_halt_decider_is_NOT_a_partial_decider_[
Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] [ succinct
]
Newsgroups: comp.theory,comp.ai.philosophy,comp.software-eng,sci.math.symbolic
References: <20210719214640.00000dfc@reddwarf.jmc> <877dhec8wh.fsf@bsb.me.uk>
<dtudnULpgO1VVWP9nZ2dnUU7-TmdnZ2d@giganews.com> <87pmv4ab6r.fsf@bsb.me.uk>
<JNadnQD-Ofr-SJz8nZ2dnUU7-XHNnZ2d@giganews.com> <871r7i6n2u.fsf@bsb.me.uk>
<OqKdnROLKJ9CdJz8nZ2dnUU7-avNnZ2d@giganews.com> <87k0la542c.fsf@bsb.me.uk>
<1NidnVPZ-NHDl5_8nZ2dnUU7-enNnZ2d@giganews.com> <87sfzw3ao1.fsf@bsb.me.uk>
<7oKdnTjx4IC20p78nZ2dnUU7-TvNnZ2d@giganews.com> <875yws36vt.fsf@bsb.me.uk>
<j66dnbdHrpV8_p78nZ2dnUU7-aXNnZ2d@giganews.com> <87im0s0ydp.fsf@bsb.me.uk>
<Brqdnfehrf0Kj5n8nZ2dnUU7-X3NnZ2d@giganews.com> <87tukblgjy.fsf@bsb.me.uk>
<qtGdnfuXs4nFOZn8nZ2dnUU7-cnNnZ2d@giganews.com> <871r7ekugt.fsf@bsb.me.uk>
<K5-dndGZo_-VmJv8nZ2dnUU78QvNnZ2d@giganews.com> <87czqxa0zk.fsf@bsb.me.uk>
<woudnXWBxPba95r8nZ2dnUU78ffNnZ2d@giganews.com> <87mtpz64sq.fsf@bsb.me.uk>
From: NoO...@NoWhere.com (olcott)
Date: Mon, 2 Aug 2021 15:53:12 -0500
User-Agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64; rv:78.0) Gecko/20100101
Thunderbird/78.12.0
MIME-Version: 1.0
In-Reply-To: <87mtpz64sq.fsf@bsb.me.uk>
Content-Type: text/plain; charset=utf-8; format=flowed
Content-Language: en-US
Content-Transfer-Encoding: 8bit
Message-ID: <w5edne8d06OkxpX8nZ2dnUU7-b_NnZ2d@giganews.com>
Lines: 135
X-Usenet-Provider: http://www.giganews.com
X-Trace: sv3-rs2JhJpHIy7aV7s4zDZorOPB1VZypPfdzyubWvS4VbToNkpILRikRw2HqOxsu4yNmUHjtwxehYIFBDN!VTg6oi+9wlJui1jpQBzhiIhELJ3pOqnHFJWaf48vGTK2LQF3P+CFDiUpcaxyZRCH8EmG9ZOkjQ==
X-Complaints-To: abuse@giganews.com
X-DMCA-Notifications: http://www.giganews.com/info/dmca.html
X-Abuse-and-DMCA-Info: Please be sure to forward a copy of ALL headers
X-Abuse-and-DMCA-Info: Otherwise we will be unable to process your complaint properly
X-Postfilter: 1.3.40
X-Original-Bytes: 7662
 by: olcott - Mon, 2 Aug 2021 20:53 UTC

On 8/2/2021 2:10 PM, Ben Bacarisse wrote:
> olcott <NoOne@NoWhere.com> writes:
>
>> On 8/1/2021 5:54 AM, Ben Bacarisse wrote:
>
>>> I am happy you have a notation you like. Are you prepared to address
>>> that fact that your H^ is not "as in Linz"?
>>
>> My Ĥ is exactly the Linz Ĥ with the additional elaboration that the
>> second wildcard state transition ⊢* is defined to be a simulating halt
>> decider.
>
> No. I've explained many times now why your Ĥ is not at all "the Linz
> Ĥ". Do you see any point in my doing so again?
>
>>> We all know you are declaring that to be correct. Here's why your Ĥ is
>>> not "as in Linz". Linz requires that
>>>
>>> Ĥ.q0 wM ⊢* Ĥ.qx wM wM ⊢* Ĥ.qn
>>> if M applied to wM does not halt
>>>
>>> Any Ĥ that eventually transitions to Ĥ.qn on input wM must do so
>>> if, and only if, the encoded M applied to wM does not halt. But you've
>>> given us a case where your Ĥ is not like this:
>>>
>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>
>> And when we eliminate the fallacy of equivocation error we have
>>
>> Ĥ[0].q0 ⟨Ĥ⟩ ⊢* Ĥ[0].qx ⟨Ĥ[1]⟩ ⟨Ĥ[2]⟩ ⊢* Ĥ[0].qn
>
> The only thing I think you are equivocating on is pretending that Ĥ[0]
> is not Ĥ, and it doesn't look as if you've removed that error. I think
> you /should/ remove it so that you can be saying something of value
> about Ĥ.
>

It is clear from the text that Linz does specify at least three
different instances of Ĥ, The TM the TMD input ⟨Ĥ⟩ and a copy of this
TMD input.

Failing to keep track of which is which when the simulated execution is
analyzed simply ignores a key salient detail.

>> The way that you do it when your twin bother commits a crime that
>> makes you guilty.
>>
>> Ĥ[0].q0 ⟨Ĥ[1]⟩ only halts because the simulation of the
>> the input to Ĥ[0].qx ⟨Ĥ[1]⟩ ⟨Ĥ[2]⟩ was aborted.
>>
>> (a) The simulation of the input to Ĥ[0].qx ⟨Ĥ[1]⟩ ⟨Ĥ[2]⟩
>> was aborted because neither ⟨Ĥ[1]⟩ nor ⟨Ĥ[2]⟩ could
>> ever possibly reach their final states.
>>
>> (b) Because neither ⟨Ĥ[1]⟩ nor ⟨Ĥ[2]⟩ could ever possibly reach
>> their final states we know that they never halt.
>>
>> (c) Because they never halt we know that Ĥ[0].qx correctly decided
>> that its input never halts.
>>
>> This is the same as: X > Y & Y > Z therefore X > Z
>> I do seem to have a correct chain of inference.
>> I do not think that you can point to any error in
>> this chain of inference.
>>
>> In an honest dialogue when you would disagree that a
>> chain of inference derives a correct conclusion you
>> would point to a specific error in this chain of inference.
>>
>> What is the error in (a)(b)(c) ?
>
> Far too many to go into all of them (if you are not inclined to correct
> anything, just jump to number 7) but ere are some:
>
> (1) Unless Ĥ[0] is just another name for Ĥ you are not saying anything I
> care about. What matters is what Ĥ applied to ⟨Ĥ⟩ does.
>
> (2) TMs don't "abort". The sequence of configurations ends.
>

This seems to diverge from an honest dialogue in that it seems like you
are saying that the concept of a simulating halt decider cannot possibly
exist.

Do you agree that a simulating halt decider can abort its simulation of
its input? If not please provide all of the details of why you disagree.

> (3) Stop talking about what "could possibly" happen. TMs do what they
> do. There are no "possibilities".
>

When the simulating halt decider at Ĥ.qx examines the behavior of its
pure simulation its input ⟨Ĥ[1]⟩ ⟨Ĥ[2]⟩ it determines that this input
never reaches its final state.

> (4) ⟨Ĥ[1]⟩ and ⟨Ĥ[2]⟩ are strings. A string does not "reach" anything.
> Strings don't even have states that can be reached. I can unravel
> this, but why must your readers work hard to unpick your metaphors?
>

The Simulation of ⟨Ĥ[1]⟩ on input ⟨Ĥ[2]⟩ is computationally equivalent
to the execution of Ĥ[1] on input ⟨Ĥ[2]⟩ thus the Simulation of ⟨Ĥ[1]⟩
either reaches or fails to reach a final state.

> (5) Ĥ[0].qx is a state. It does not decide anything. (Again, I can
> guess what you mean but you asked for help.)
>

Ĥ[0].qx is stipulated to be the halt decider named H.
In the erroneous Linz notation it is at the second start state of Ĥ.

> (6) States don't have input. Whilst I could guess that you mean "the
> tape" at the point the state is entered", states in a TM may be
> entered many times so there is no obvious single "input".
>

Linz refers to it as: "The input to H" thus making your "correction"
within the context of Linz, incorrect.

> (7) The correct behaviour of Ĥ is not based on (a) and (b) but on what
> Linz says about Ĥ applied to ⟨Ĥ⟩. Your Ĥ does not behave as Linz's
> Ĥ should, even in the one case you care about.

You slightly changed the subject. We are not talking about the behavior
of Ĥ. We are talking about what the future behavior of the input to the
simulating halt decider at Ĥ.qx would be.

When we stay 100% perfectly focused on exactly this we can see that the
future behavior of the input to Ĥ.qx never reaches its final state.

--
Copyright 2021 Pete Olcott

"Great spirits have always encountered violent opposition from mediocre
minds." Einstein

Re: Black box halt decider is NOT a partial decider [ Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] [ succinct ]

<87bl6f5qvy.fsf@bsb.me.uk>

 copy mid

https://www.novabbs.com/devel/article-flat.php?id=19382&group=comp.theory#19382

 copy link   Newsgroups: comp.theory
Path: i2pn2.org!i2pn.org!eternal-september.org!reader02.eternal-september.org!.POSTED!not-for-mail
From: ben.use...@bsb.me.uk (Ben Bacarisse)
Newsgroups: comp.theory
Subject: Re: Black box halt decider is NOT a partial decider [
Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] [
succinct ]
Date: Tue, 03 Aug 2021 01:11:13 +0100
Organization: A noiseless patient Spider
Lines: 78
Message-ID: <87bl6f5qvy.fsf@bsb.me.uk>
References: <20210719214640.00000dfc@reddwarf.jmc> <87pmv4ab6r.fsf@bsb.me.uk>
<JNadnQD-Ofr-SJz8nZ2dnUU7-XHNnZ2d@giganews.com>
<871r7i6n2u.fsf@bsb.me.uk>
<OqKdnROLKJ9CdJz8nZ2dnUU7-avNnZ2d@giganews.com>
<87k0la542c.fsf@bsb.me.uk>
<1NidnVPZ-NHDl5_8nZ2dnUU7-enNnZ2d@giganews.com>
<87sfzw3ao1.fsf@bsb.me.uk>
<7oKdnTjx4IC20p78nZ2dnUU7-TvNnZ2d@giganews.com>
<875yws36vt.fsf@bsb.me.uk>
<j66dnbdHrpV8_p78nZ2dnUU7-aXNnZ2d@giganews.com>
<87im0s0ydp.fsf@bsb.me.uk>
<Brqdnfehrf0Kj5n8nZ2dnUU7-X3NnZ2d@giganews.com>
<87tukblgjy.fsf@bsb.me.uk>
<qtGdnfuXs4nFOZn8nZ2dnUU7-cnNnZ2d@giganews.com>
<871r7ekugt.fsf@bsb.me.uk>
<K5-dndGZo_-VmJv8nZ2dnUU78QvNnZ2d@giganews.com>
<87czqxa0zk.fsf@bsb.me.uk>
<woudnXWBxPba95r8nZ2dnUU78ffNnZ2d@giganews.com>
<87mtpz64sq.fsf@bsb.me.uk>
<w5edne8d06OkxpX8nZ2dnUU7-b_NnZ2d@giganews.com>
Mime-Version: 1.0
Content-Type: text/plain; charset=utf-8
Content-Transfer-Encoding: 8bit
Injection-Info: reader02.eternal-september.org; posting-host="cd4185fe0fda946c38ad1260f6402832";
logging-data="6758"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX196PBDdD4ZAMbb9K4FC6bupL+twjwT2r40="
Cancel-Lock: sha1:i/wG2M4DhH8nBNx0mOGEVf1H+tU=
sha1:5WDq0nzGcTsqTbJGkm+u0Qk8vnU=
X-BSB-Auth: 1.a7ae967720993217ef47.20210803011113BST.87bl6f5qvy.fsf@bsb.me.uk
 by: Ben Bacarisse - Tue, 3 Aug 2021 00:11 UTC

olcott <NoOne@NoWhere.com> writes:

> On 8/2/2021 2:10 PM, Ben Bacarisse wrote:
>> olcott <NoOne@NoWhere.com> writes:
>>
>>> On 8/1/2021 5:54 AM, Ben Bacarisse wrote:
>>
>>>> I am happy you have a notation you like. Are you prepared to address
>>>> that fact that your H^ is not "as in Linz"?
>>>
>>> My Ĥ is exactly the Linz Ĥ with the additional elaboration that the
>>> second wildcard state transition ⊢* is defined to be a simulating halt
>>> decider.
>> No. I've explained many times now why your Ĥ is not at all "the Linz
>> Ĥ". Do you see any point in my doing so again?

I suspect not. You certainly have not asked a single question that
could help you to understand why your Ĥ is irrelevant.

>>>> We all know you are declaring that to be correct. Here's why your Ĥ is
>>>> not "as in Linz". Linz requires that
>>>>
>>>> Ĥ.q0 wM ⊢* Ĥ.qx wM wM ⊢* Ĥ.qn
>>>> if M applied to wM does not halt
>>>>
>>>> Any Ĥ that eventually transitions to Ĥ.qn on input wM must do so
>>>> if, and only if, the encoded M applied to wM does not halt. But you've
>>>> given us a case where your Ĥ is not like this:
>>>>
>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>>
>>> And when we eliminate the fallacy of equivocation error we have
>>>
>>> Ĥ[0].q0 ⟨Ĥ⟩ ⊢* Ĥ[0].qx ⟨Ĥ[1]⟩ ⟨Ĥ[2]⟩ ⊢* Ĥ[0].qn
>> The only thing I think you are equivocating on is pretending that Ĥ[0]
>> is not Ĥ, and it doesn't look as if you've removed that error. I think
>> you /should/ remove it so that you can be saying something of value
>> about Ĥ.
>
> It is clear from the text that Linz does specify at least three
> different instances of Ĥ, The TM the TMD input ⟨Ĥ⟩ and a copy of this
> TMD input.

Still equivocating. Either Ĥ[0] = Ĥ or you are wasting everyone's time.

(This is mathematical equality. Ĥ is a tuple of sets. If Ĥ[0] is not
exactly identical in every way to Ĥ then I don't care about it. Note
that I'm not disputing your right, for ease of explanation, to give
identical things more than one name. But the same permission allows me
to use any of the names because they name the same thing.)

You are wrong because

Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qn

where Linz requires that

Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qn
if (and only if) Ĥ applied to ⟨Ĥ⟩ does not halt.

Either you ask questions that might help you to understand what I'm
saying, or you can just repeat again, in ever greater detail, what
happens in that ⊢* as if the exact way in which you are wrong is the key
thing you want to tell the world. It's up to you.

Please don't think I don't know what you are saying. I understand all
the copying and levels and so on. But the details don't make you right
because it's the outcome that makes you wrong. No explanation of how
you get the wrong behaviour, no matter how detailed, makes the wrong
behaviour right. Your Ĥ is just one of countless other TMs that do not
do what Linz says is impossible, even for this one input.

I'll leave it there. If you really want my comments on your replies to
the errors you asked me to point it, I'll post again, but it it's all
noise compared to the big mistake.

--
Ben.

Re: Black box halt decider is NOT a partial decider [ Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] ( Are you game ? )

<875ywn5qfr.fsf@bsb.me.uk>

 copy mid

https://www.novabbs.com/devel/article-flat.php?id=19383&group=comp.theory#19383

 copy link   Newsgroups: comp.theory
Path: i2pn2.org!i2pn.org!eternal-september.org!reader02.eternal-september.org!.POSTED!not-for-mail
From: ben.use...@bsb.me.uk (Ben Bacarisse)
Newsgroups: comp.theory
Subject: Re: Black box halt decider is NOT a partial decider [
Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] (
Are you game ? )
Date: Tue, 03 Aug 2021 01:20:56 +0100
Organization: A noiseless patient Spider
Lines: 74
Message-ID: <875ywn5qfr.fsf@bsb.me.uk>
References: <20210719214640.00000dfc@reddwarf.jmc> <877dhec8wh.fsf@bsb.me.uk>
<dtudnULpgO1VVWP9nZ2dnUU7-TmdnZ2d@giganews.com>
<87pmv4ab6r.fsf@bsb.me.uk>
<JNadnQD-Ofr-SJz8nZ2dnUU7-XHNnZ2d@giganews.com>
<871r7i6n2u.fsf@bsb.me.uk>
<OqKdnROLKJ9CdJz8nZ2dnUU7-avNnZ2d@giganews.com>
<87k0la542c.fsf@bsb.me.uk>
<x5mdnTC66uNJip_8nZ2dnUU7-aWdnZ2d@giganews.com>
<87mtq438ge.fsf@bsb.me.uk>
<PbednTcmR4_Mw578nZ2dnUU78WvNnZ2d@giganews.com>
<87tukc12yh.fsf@bsb.me.uk>
<e6OdnW_rdvusk5n8nZ2dnUU7-dPNnZ2d@giganews.com>
<875ywrmwsr.fsf@bsb.me.uk>
<GtmdnfBrysPrAZn8nZ2dnUU7-L_NnZ2d@giganews.com>
<874kcakv3d.fsf@bsb.me.uk>
<-M-dnfsXl4WvWpj8nZ2dnUU7-IGdnZ2d@giganews.com>
<87im0pa1pp.fsf@bsb.me.uk>
<6eOdnaoMUdZN_pr8nZ2dnUU7-cPNnZ2d@giganews.com>
<87y29j6c5e.fsf@bsb.me.uk>
<p8SdnV8dJu3wq5X8nZ2dnUU7-a3NnZ2d@giganews.com>
Mime-Version: 1.0
Content-Type: text/plain; charset=utf-8
Content-Transfer-Encoding: 8bit
Injection-Info: reader02.eternal-september.org; posting-host="cd4185fe0fda946c38ad1260f6402832";
logging-data="6758"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/ugi2WJCBEGDhE1IWk2CSC2C6tDgge9Bg="
Cancel-Lock: sha1:vRKPVqKZ/sBtZW9jbSeJf+OU6tQ=
sha1:yAiQIeLkk6drdloQnOuqftQsSQY=
X-BSB-Auth: 1.feeab6e149b77be99fc3.20210803012056BST.875ywn5qfr.fsf@bsb.me.uk
 by: Ben Bacarisse - Tue, 3 Aug 2021 00:20 UTC

olcott <NoOne@NoWhere.com> writes:

> On 8/2/2021 11:31 AM, Ben Bacarisse wrote:
>> olcott <NoOne@NoWhere.com> writes:
>>
>>> On 8/1/2021 5:39 AM, Ben Bacarisse wrote:
>>>> olcott <NoOne@NoWhere.com> writes:
>>>>
>>>>> On 7/31/2021 4:54 PM, Ben Bacarisse wrote:
>>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>>
>>>>>>> It matters not what I had.
>>>>>> Because you can't justify it the honest debate you claim to want.
>>>>>>
>>>>>>> It only matters what I have.
>>>>>> I.e. nothing of any interest. You make it plain in a previous reply
>>>>>> that you've had nothing of interest going right back to the original
>>>>>> deceptive claim.
>>>>>>
>>>>>>> If you are sincere about an honest dialogue then we must quit focusing
>>>>>>> on details of obsolete technology.
>>>>>> And yet you skipped the big picture part:
>>>>>>
>>>>>>>> (5) You said you had "an H that decides (Ĥ, Ĥ)". What decision did your
>>>>>>>> Dec 2018 code come to about "(Ĥ, Ĥ)"?
>>>>>>>
>>>>>>> The 2018 version Halts(H_Hat, H_Hat)==0 in the exact same way that
>>>>>>> H(P,P)==0 now except that the never halting criteria is much more
>>>>>>> elaborate. The initial criteria was very crude.
>>>>>>
>>>>>> Ah, so you never had H and H_Hat that do anything that anyone would say
>>>>>> is impossible. Had you said, back in Dec 2018, "I have C code such that
>>>>>> H(H_Hat, H_Hat) == 0 but H_Hat(H_Hat) halts" no one would have been
>>>>>> interested.
>>>>>
>>>>> If you are sincere about an honest dialogue then we must quit focusing
>>>>> on details of obsolete technology.
>>>>
>>>> Ah, an honest dialogue requires me to ignore your past deception? Well,
>>>> I can accommodate that: you /currently/ don't have anything that anyone
>>>> would consider to be impossible or even interesting. An H/H_Hat pair
>>>> such that H(H_Hat, H_Hat) == 0 and H_Hat(H_Hat) halts is of no interest
>>>> to anyone. Is that better?
>>>
>>> When H is a simulating partial halt decider and the halt decider
>>> embedded in Ĥ at Ĥ.qx is a simulating halt decider then:
>>>
>>> It is the case that the input to H(P,P) and the input to Ĥ(⟨Ĥ⟩) cannot
>>> possibly ever reach their final state and must have their simulation
>>> aborted to prevent the infinite execution of P and Ĥ.
>>>
>>> Let's have an honest dialogue about that.
>>
>> Yes, let's. Here's how to say what happens without all those vague
>> (and, frankly, incorrect) words:
>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>> If you don't mean
>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>> can you say what you do mean formally? Formally means using some
>> formal notation like Linz does.
>
> As Linz already specifies yet does not encode in his notation there
> are at least three separate and distinct instances of Ĥ.

You are not replying to my remarks. Anyway, I've posted at more length
elsewhere the same point that you keep side-stepping. I think the
pattern is set: I'll keep accepting (even when it's wrong) what you say
happens /before/ Ĥ(⟨Ĥ⟩) transitions to Ĥ.qn, and you'll keep ignoring
why Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qn shows your Ĥ is irrelevant.

I don't think progress can be made like that.

--
Ben.

Re: Black box halt decider is NOT a partial decider [ Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] [ succinct ]

<xLednaPs_ZSXCZX8nZ2dnUU7-YnNnZ2d@giganews.com>

 copy mid

https://www.novabbs.com/devel/article-flat.php?id=19385&group=comp.theory#19385

 copy link   Newsgroups: comp.theory comp.ai.philosophy sci.math.symbolic comp.software-eng
Path: i2pn2.org!i2pn.org!weretis.net!feeder8.news.weretis.net!news.uzoreto.com!tr1.eu1.usenetexpress.com!feeder.usenetexpress.com!tr3.iad1.usenetexpress.com!border1.nntp.dca1.giganews.com!nntp.giganews.com!buffer1.nntp.dca1.giganews.com!news.giganews.com.POSTED!not-for-mail
NNTP-Posting-Date: Mon, 02 Aug 2021 19:55:38 -0500
Subject: Re:_Black_box_halt_decider_is_NOT_a_partial_decider_[ Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] [ succinct ]
Newsgroups: comp.theory,comp.ai.philosophy,sci.math.symbolic,comp.software-eng
References: <20210719214640.00000dfc@reddwarf.jmc> <87pmv4ab6r.fsf@bsb.me.uk> <JNadnQD-Ofr-SJz8nZ2dnUU7-XHNnZ2d@giganews.com> <871r7i6n2u.fsf@bsb.me.uk> <OqKdnROLKJ9CdJz8nZ2dnUU7-avNnZ2d@giganews.com> <87k0la542c.fsf@bsb.me.uk> <1NidnVPZ-NHDl5_8nZ2dnUU7-enNnZ2d@giganews.com> <87sfzw3ao1.fsf@bsb.me.uk> <7oKdnTjx4IC20p78nZ2dnUU7-TvNnZ2d@giganews.com> <875yws36vt.fsf@bsb.me.uk> <j66dnbdHrpV8_p78nZ2dnUU7-aXNnZ2d@giganews.com> <87im0s0ydp.fsf@bsb.me.uk> <Brqdnfehrf0Kj5n8nZ2dnUU7-X3NnZ2d@giganews.com> <87tukblgjy.fsf@bsb.me.uk> <qtGdnfuXs4nFOZn8nZ2dnUU7-cnNnZ2d@giganews.com> <871r7ekugt.fsf@bsb.me.uk> <K5-dndGZo_-VmJv8nZ2dnUU78QvNnZ2d@giganews.com> <87czqxa0zk.fsf@bsb.me.uk> <woudnXWBxPba95r8nZ2dnUU78ffNnZ2d@giganews.com> <87mtpz64sq.fsf@bsb.me.uk> <w5edne8d06OkxpX8nZ2dnUU7-b_NnZ2d@giganews.com> <87bl6f5qvy.fsf@bsb.me.uk>
From: NoO...@NoWhere.com (olcott)
Date: Mon, 2 Aug 2021 19:55:37 -0500
User-Agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64; rv:78.0) Gecko/20100101 Thunderbird/78.12.0
MIME-Version: 1.0
In-Reply-To: <87bl6f5qvy.fsf@bsb.me.uk>
Content-Type: text/plain; charset=utf-8; format=flowed
Content-Language: en-US
Content-Transfer-Encoding: 8bit
Message-ID: <xLednaPs_ZSXCZX8nZ2dnUU7-YnNnZ2d@giganews.com>
Lines: 112
X-Usenet-Provider: http://www.giganews.com
X-Trace: sv3-gBd5mi8CdLbspcVOiomxbzfc5n2juVNqPSVxGw/A2huHcZNxvBEIYm/9miecpoc8NRebmryz6r6SdjG!EqDNoEN71uHLUorm4HjR9kn8yh+gqTLR8WHr9nqgC+/pdTi3gPkMhLn7/+Ehc942sUKmwOxoIQ==
X-Complaints-To: abuse@giganews.com
X-DMCA-Notifications: http://www.giganews.com/info/dmca.html
X-Abuse-and-DMCA-Info: Please be sure to forward a copy of ALL headers
X-Abuse-and-DMCA-Info: Otherwise we will be unable to process your complaint properly
X-Postfilter: 1.3.40
X-Original-Bytes: 6655
 by: olcott - Tue, 3 Aug 2021 00:55 UTC

On 8/2/2021 7:11 PM, Ben Bacarisse wrote:
> olcott <NoOne@NoWhere.com> writes:
>
>> On 8/2/2021 2:10 PM, Ben Bacarisse wrote:
>>> olcott <NoOne@NoWhere.com> writes:
>>>
>>>> On 8/1/2021 5:54 AM, Ben Bacarisse wrote:
>>>
>>>>> I am happy you have a notation you like. Are you prepared to address
>>>>> that fact that your H^ is not "as in Linz"?
>>>>
>>>> My Ĥ is exactly the Linz Ĥ with the additional elaboration that the
>>>> second wildcard state transition ⊢* is defined to be a simulating halt
>>>> decider.
>>> No. I've explained many times now why your Ĥ is not at all "the Linz
>>> Ĥ". Do you see any point in my doing so again?
>
> I suspect not. You certainly have not asked a single question that
> could help you to understand why your Ĥ is irrelevant.
>
>>>>> We all know you are declaring that to be correct. Here's why your Ĥ is
>>>>> not "as in Linz". Linz requires that
>>>>>
>>>>> Ĥ.q0 wM ⊢* Ĥ.qx wM wM ⊢* Ĥ.qn
>>>>> if M applied to wM does not halt
>>>>>
>>>>> Any Ĥ that eventually transitions to Ĥ.qn on input wM must do so
>>>>> if, and only if, the encoded M applied to wM does not halt. But you've
>>>>> given us a case where your Ĥ is not like this:
>>>>>
>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>>>
>>>> And when we eliminate the fallacy of equivocation error we have
>>>>
>>>> Ĥ[0].q0 ⟨Ĥ⟩ ⊢* Ĥ[0].qx ⟨Ĥ[1]⟩ ⟨Ĥ[2]⟩ ⊢* Ĥ[0].qn
>>> The only thing I think you are equivocating on is pretending that Ĥ[0]
>>> is not Ĥ, and it doesn't look as if you've removed that error. I think
>>> you /should/ remove it so that you can be saying something of value
>>> about Ĥ.
>>
>> It is clear from the text that Linz does specify at least three
>> different instances of Ĥ, The TM the TMD input ⟨Ĥ⟩ and a copy of this
>> TMD input.
>
> Still equivocating. Either Ĥ[0] = Ĥ or you are wasting everyone's time.
>

Ĥ[0] = Ĥ
Ĥ[1] != Ĥ
Ĥ[2] != Ĥ

> (This is mathematical equality. Ĥ is a tuple of sets. If Ĥ[0] is not
> exactly identical in every way to Ĥ then I don't care about it. Note

The different instances of Ĥ are different in a crucial way and that is
their placement in the execution trace.

> that I'm not disputing your right, for ease of explanation, to give
> identical things more than one name. But the same permission allows me
> to use any of the names because they name the same thing.)
>

Only because their differing placement in the execution trace do they
have different halting behavior. This is a crucial distinction.

> You are wrong because
>
> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qn
>
> where Linz requires that
>
> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qn
> if (and only if) Ĥ applied to ⟨Ĥ⟩ does not halt.
>

Linz could require that all cats must be dogs, the verifiable fact is
that the input ⟨Ĥ⟩ ⟨Ĥ⟩ to Ĥ.qx is correctly decided as never halting.

If you really do sincerely want an actual honest dialogue you would
carefully work through all the steps to confirm that the input ⟨Ĥ⟩ ⟨Ĥ⟩
to Ĥ.qx never halts.

Once we have mutual agreement that Ĥ.qx correctly decides that its
input: ⟨Ĥ⟩ ⟨Ĥ⟩ never halts and Ĥ does halt, then we have the basis to go
to the next step and resolve the actual paradox.

As long as it is simply dismissed out-of-hand as a contradiction the
paradox remains unresolved.

> Either you ask questions that might help you to understand what I'm
> saying, or you can just repeat again, in ever greater detail, what
> happens in that ⊢* as if the exact way in which you are wrong is the key
> thing you want to tell the world. It's up to you.
>
> Please don't think I don't know what you are saying. I understand all
> the copying and levels and so on. But the details don't make you right
> because it's the outcome that makes you wrong. No explanation of how
> you get the wrong behaviour, no matter how detailed, makes the wrong
> behaviour right. Your Ĥ is just one of countless other TMs that do not
> do what Linz says is impossible, even for this one input.
>
> I'll leave it there. If you really want my comments on your replies to
> the errors you asked me to point it, I'll post again, but it it's all
> noise compared to the big mistake.
>

--
Copyright 2021 Pete Olcott

"Great spirits have always encountered violent opposition from mediocre
minds." Einstein

Re: Black box halt decider is NOT a partial decider [ Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] ( Are you game ? )

<hJmdnSWv8-zPCJX8nZ2dnUU7-T_NnZ2d@giganews.com>

 copy mid

https://www.novabbs.com/devel/article-flat.php?id=19386&group=comp.theory#19386

 copy link   Newsgroups: comp.theory
Path: i2pn2.org!rocksolid2!i2pn.org!weretis.net!feeder8.news.weretis.net!feeder1.feed.usenet.farm!feed.usenet.farm!tr3.eu1.usenetexpress.com!feeder.usenetexpress.com!tr2.iad1.usenetexpress.com!border1.nntp.dca1.giganews.com!nntp.giganews.com!buffer1.nntp.dca1.giganews.com!news.giganews.com.POSTED!not-for-mail
NNTP-Posting-Date: Mon, 02 Aug 2021 20:01:06 -0500
Subject: Re:_Black_box_halt_decider_is_NOT_a_partial_decider_[ Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] ( Are you game_?_)
Newsgroups: comp.theory
References: <20210719214640.00000dfc@reddwarf.jmc> <877dhec8wh.fsf@bsb.me.uk> <dtudnULpgO1VVWP9nZ2dnUU7-TmdnZ2d@giganews.com> <87pmv4ab6r.fsf@bsb.me.uk> <JNadnQD-Ofr-SJz8nZ2dnUU7-XHNnZ2d@giganews.com> <871r7i6n2u.fsf@bsb.me.uk> <OqKdnROLKJ9CdJz8nZ2dnUU7-avNnZ2d@giganews.com> <87k0la542c.fsf@bsb.me.uk> <x5mdnTC66uNJip_8nZ2dnUU7-aWdnZ2d@giganews.com> <87mtq438ge.fsf@bsb.me.uk> <PbednTcmR4_Mw578nZ2dnUU78WvNnZ2d@giganews.com> <87tukc12yh.fsf@bsb.me.uk> <e6OdnW_rdvusk5n8nZ2dnUU7-dPNnZ2d@giganews.com> <875ywrmwsr.fsf@bsb.me.uk> <GtmdnfBrysPrAZn8nZ2dnUU7-L_NnZ2d@giganews.com> <874kcakv3d.fsf@bsb.me.uk> <-M-dnfsXl4WvWpj8nZ2dnUU7-IGdnZ2d@giganews.com> <87im0pa1pp.fsf@bsb.me.uk> <6eOdnaoMUdZN_pr8nZ2dnUU7-cPNnZ2d@giganews.com> <87y29j6c5e.fsf@bsb.me.uk> <p8SdnV8dJu3wq5X8nZ2dnUU7-a3NnZ2d@giganews.com> <875ywn5qfr.fsf@bsb.me.uk>
From: NoO...@NoWhere.com (olcott)
Date: Mon, 2 Aug 2021 20:01:05 -0500
User-Agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64; rv:78.0) Gecko/20100101 Thunderbird/78.12.0
MIME-Version: 1.0
In-Reply-To: <875ywn5qfr.fsf@bsb.me.uk>
Content-Type: text/plain; charset=utf-8; format=flowed
Content-Language: en-US
Content-Transfer-Encoding: 8bit
Message-ID: <hJmdnSWv8-zPCJX8nZ2dnUU7-T_NnZ2d@giganews.com>
Lines: 89
X-Usenet-Provider: http://www.giganews.com
X-Trace: sv3-BX4NjhVP3GIgK8tb1uWuB2w1QyDkyoSKBSzlhMsFIO9Pv8iAICIs+4UesLVCwu91aYNTV5CS4lBnY9M!miaD+yfolaWKea7jXN+OPQ3kG5auwl33JEpnRMkYZMVH1kCg54CFU5J2Py7THLiORFuG7iXEbA==
X-Complaints-To: abuse@giganews.com
X-DMCA-Notifications: http://www.giganews.com/info/dmca.html
X-Abuse-and-DMCA-Info: Please be sure to forward a copy of ALL headers
X-Abuse-and-DMCA-Info: Otherwise we will be unable to process your complaint properly
X-Postfilter: 1.3.40
X-Original-Bytes: 6041
 by: olcott - Tue, 3 Aug 2021 01:01 UTC

On 8/2/2021 7:20 PM, Ben Bacarisse wrote:
> olcott <NoOne@NoWhere.com> writes:
>
>> On 8/2/2021 11:31 AM, Ben Bacarisse wrote:
>>> olcott <NoOne@NoWhere.com> writes:
>>>
>>>> On 8/1/2021 5:39 AM, Ben Bacarisse wrote:
>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>
>>>>>> On 7/31/2021 4:54 PM, Ben Bacarisse wrote:
>>>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>>>
>>>>>>>> It matters not what I had.
>>>>>>> Because you can't justify it the honest debate you claim to want.
>>>>>>>
>>>>>>>> It only matters what I have.
>>>>>>> I.e. nothing of any interest. You make it plain in a previous reply
>>>>>>> that you've had nothing of interest going right back to the original
>>>>>>> deceptive claim.
>>>>>>>
>>>>>>>> If you are sincere about an honest dialogue then we must quit focusing
>>>>>>>> on details of obsolete technology.
>>>>>>> And yet you skipped the big picture part:
>>>>>>>
>>>>>>>>> (5) You said you had "an H that decides (Ĥ, Ĥ)". What decision did your
>>>>>>>>> Dec 2018 code come to about "(Ĥ, Ĥ)"?
>>>>>>>>
>>>>>>>> The 2018 version Halts(H_Hat, H_Hat)==0 in the exact same way that
>>>>>>>> H(P,P)==0 now except that the never halting criteria is much more
>>>>>>>> elaborate. The initial criteria was very crude.
>>>>>>>
>>>>>>> Ah, so you never had H and H_Hat that do anything that anyone would say
>>>>>>> is impossible. Had you said, back in Dec 2018, "I have C code such that
>>>>>>> H(H_Hat, H_Hat) == 0 but H_Hat(H_Hat) halts" no one would have been
>>>>>>> interested.
>>>>>>
>>>>>> If you are sincere about an honest dialogue then we must quit focusing
>>>>>> on details of obsolete technology.
>>>>>
>>>>> Ah, an honest dialogue requires me to ignore your past deception? Well,
>>>>> I can accommodate that: you /currently/ don't have anything that anyone
>>>>> would consider to be impossible or even interesting. An H/H_Hat pair
>>>>> such that H(H_Hat, H_Hat) == 0 and H_Hat(H_Hat) halts is of no interest
>>>>> to anyone. Is that better?
>>>>
>>>> When H is a simulating partial halt decider and the halt decider
>>>> embedded in Ĥ at Ĥ.qx is a simulating halt decider then:
>>>>
>>>> It is the case that the input to H(P,P) and the input to Ĥ(⟨Ĥ⟩) cannot
>>>> possibly ever reach their final state and must have their simulation
>>>> aborted to prevent the infinite execution of P and Ĥ.
>>>>
>>>> Let's have an honest dialogue about that.
>>>
>>> Yes, let's. Here's how to say what happens without all those vague
>>> (and, frankly, incorrect) words:
>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>> If you don't mean
>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>> can you say what you do mean formally? Formally means using some
>>> formal notation like Linz does.
>>
>> As Linz already specifies yet does not encode in his notation there
>> are at least three separate and distinct instances of Ĥ.
>
> You are not replying to my remarks. Anyway, I've posted at more length
> elsewhere the same point that you keep side-stepping. I think the
> pattern is set: I'll keep accepting (even when it's wrong) what you say
> happens /before/ Ĥ(⟨Ĥ⟩) transitions to Ĥ.qn, and you'll keep ignoring
> why Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qn shows your Ĥ is irrelevant.
>
> I don't think progress can be made like that.
>

As long as you keep thinking of it as a resolved contradiction the
actual paradox remains unresolved.

I proved that Ĥ.qx does correctly decide that its input ⟨Ĥ⟩ ⟨Ĥ⟩ never
halts it is also equally proven that Ĥ halts thus a paradox and not a
contradiction is formed.

My current answer to this is GIGO self-contradictory input <IN>
contractory output <OUT>. There may be a better answer.

--
Copyright 2021 Pete Olcott

"Great spirits have always encountered violent opposition from mediocre
minds." Einstein

Re: Black box halt decider is NOT a partial decider [ Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] [ succinct ]

<87o8af47y0.fsf@bsb.me.uk>

 copy mid

https://www.novabbs.com/devel/article-flat.php?id=19388&group=comp.theory#19388

 copy link   Newsgroups: comp.theory
Followup: comp.theory
Path: i2pn2.org!i2pn.org!eternal-september.org!reader02.eternal-september.org!.POSTED!not-for-mail
From: ben.use...@bsb.me.uk (Ben Bacarisse)
Newsgroups: comp.theory
Subject: Re: Black box halt decider is NOT a partial decider [
Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] [
succinct ]
Followup-To: comp.theory
Date: Tue, 03 Aug 2021 02:45:43 +0100
Organization: A noiseless patient Spider
Lines: 145
Message-ID: <87o8af47y0.fsf@bsb.me.uk>
References: <20210719214640.00000dfc@reddwarf.jmc> <871r7i6n2u.fsf@bsb.me.uk>
<OqKdnROLKJ9CdJz8nZ2dnUU7-avNnZ2d@giganews.com>
<87k0la542c.fsf@bsb.me.uk>
<1NidnVPZ-NHDl5_8nZ2dnUU7-enNnZ2d@giganews.com>
<87sfzw3ao1.fsf@bsb.me.uk>
<7oKdnTjx4IC20p78nZ2dnUU7-TvNnZ2d@giganews.com>
<875yws36vt.fsf@bsb.me.uk>
<j66dnbdHrpV8_p78nZ2dnUU7-aXNnZ2d@giganews.com>
<87im0s0ydp.fsf@bsb.me.uk>
<Brqdnfehrf0Kj5n8nZ2dnUU7-X3NnZ2d@giganews.com>
<87tukblgjy.fsf@bsb.me.uk>
<qtGdnfuXs4nFOZn8nZ2dnUU7-cnNnZ2d@giganews.com>
<871r7ekugt.fsf@bsb.me.uk>
<K5-dndGZo_-VmJv8nZ2dnUU78QvNnZ2d@giganews.com>
<87czqxa0zk.fsf@bsb.me.uk>
<woudnXWBxPba95r8nZ2dnUU78ffNnZ2d@giganews.com>
<87mtpz64sq.fsf@bsb.me.uk>
<w5edne8d06OkxpX8nZ2dnUU7-b_NnZ2d@giganews.com>
<87bl6f5qvy.fsf@bsb.me.uk>
<xLednaPs_ZSXCZX8nZ2dnUU7-YnNnZ2d@giganews.com>
Mime-Version: 1.0
Content-Type: text/plain; charset=utf-8
Content-Transfer-Encoding: 8bit
Injection-Info: reader02.eternal-september.org; posting-host="cd4185fe0fda946c38ad1260f6402832";
logging-data="3190"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1+SyQJDCZ4qPq8+lgWt4HmF/etgO3oGTYU="
Cancel-Lock: sha1:gt+3Ns2w12tzWrz9FNL/yiUTu6c=
sha1:QTLcWju5Z+S3+RXQ3xIoB/nfuwk=
X-BSB-Auth: 1.b9181e25e9bb8cc2705e.20210803024543BST.87o8af47y0.fsf@bsb.me.uk
 by: Ben Bacarisse - Tue, 3 Aug 2021 01:45 UTC

olcott <NoOne@NoWhere.com> writes:

> On 8/2/2021 7:11 PM, Ben Bacarisse wrote:
>> olcott <NoOne@NoWhere.com> writes:
>>
>>> On 8/2/2021 2:10 PM, Ben Bacarisse wrote:
>>>> olcott <NoOne@NoWhere.com> writes:
>>>>
>>>>> On 8/1/2021 5:54 AM, Ben Bacarisse wrote:
>>>>
>>>>>> I am happy you have a notation you like. Are you prepared to address
>>>>>> that fact that your H^ is not "as in Linz"?
>>>>>
>>>>> My Ĥ is exactly the Linz Ĥ with the additional elaboration that the
>>>>> second wildcard state transition ⊢* is defined to be a simulating halt
>>>>> decider.
>>>> No. I've explained many times now why your Ĥ is not at all "the Linz
>>>> Ĥ". Do you see any point in my doing so again?
>> I suspect not. You certainly have not asked a single question that
>> could help you to understand why your Ĥ is irrelevant.
>>
>>>>>> We all know you are declaring that to be correct. Here's why your Ĥ is
>>>>>> not "as in Linz". Linz requires that
>>>>>>
>>>>>> Ĥ.q0 wM ⊢* Ĥ.qx wM wM ⊢* Ĥ.qn
>>>>>> if M applied to wM does not halt
>>>>>>
>>>>>> Any Ĥ that eventually transitions to Ĥ.qn on input wM must do so
>>>>>> if, and only if, the encoded M applied to wM does not halt. But you've
>>>>>> given us a case where your Ĥ is not like this:
>>>>>>
>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>>>>
>>>>> And when we eliminate the fallacy of equivocation error we have
>>>>>
>>>>> Ĥ[0].q0 ⟨Ĥ⟩ ⊢* Ĥ[0].qx ⟨Ĥ[1]⟩ ⟨Ĥ[2]⟩ ⊢* Ĥ[0].qn
>>>> The only thing I think you are equivocating on is pretending that Ĥ[0]
>>>> is not Ĥ, and it doesn't look as if you've removed that error. I think
>>>> you /should/ remove it so that you can be saying something of value
>>>> about Ĥ.
>>>
>>> It is clear from the text that Linz does specify at least three
>>> different instances of Ĥ, The TM the TMD input ⟨Ĥ⟩ and a copy of this
>>> TMD input.
>> Still equivocating. Either Ĥ[0] = Ĥ or you are wasting everyone's time.
>>
>
> Ĥ[0] = Ĥ
> Ĥ[1] != Ĥ
> Ĥ[2] != Ĥ

Switching to the strings, if ⟨Ĥ[1]⟩ != ⟨Ĥ⟩ or ⟨Ĥ[2]⟩ != ⟨Ĥ⟩ then your Ĥ
is not built using the correct rules. That's up to you, but you did
once claim to be addressing the proof in Linz.

Switching back to TMs, two equal strings, like ⟨Ĥ[1]⟩ and ⟨Ĥ⟩, can't
encode unequal TMs.

But, as usual, this is a side error. It had nothing to do with why your
Ĥ is irrelevant but perhaps you hope to coax the world down this
rabbit hole so the big mistake goes unnoticed.

(I note that since you are using symbols here, it's possible the three
formulas above might just be math poems. You might be use equality and
non-equality in some metaphorical sense.)

>> (This is mathematical equality. Ĥ is a tuple of sets. If Ĥ[0] is not
>> exactly identical in every way to Ĥ then I don't care about it. Note
>
> The different instances of Ĥ are different in a crucial way and that
> is their placement in the execution trace.

You suggest above that you have multiple non-equal TMs. That's not how
the "hat" construction works.

>> that I'm not disputing your right, for ease of explanation, to give
>> identical things more than one name. But the same permission allows me
>> to use any of the names because they name the same thing.)
>
> Only because their differing placement in the execution trace do they
> have different halting behavior. This is a crucial distinction.

Again an irrelevant rabbit hole that I suspect you'd like me to follow
you down.

>> You are wrong because
>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qn
>> where Linz requires that
>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qn
>> if (and only if) Ĥ applied to ⟨Ĥ⟩ does not halt.
>
> Linz could require that all cats must be dogs,

I suppose so. And if you claimed that you had a cat "exactly and
precisely as in Linz" you'd have to show it was dog. If you couldn't,
you might agree that Linz's cat-dogs don't exist. After all, he doesn't
think they exist either, so it's easy to agree with him.

Anyway, It appears you think that Linz's Ĥs that transitions to qn if
(and only if) Ĥ applied to ⟨Ĥ⟩ does not halt are as impossible as his
cat-dogs. Great. You are correct.

You once claimed to have a TM "exactly and precisely as in Linz" that
everyone else was claiming to be impossible. You don't anymore. You
now have an Ĥ that does something entirely mundane, namely

Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qn
if Ĥ applied to ⟨Ĥ⟩ halts.

Such TMs are ten-a-penny, though most are probably nothing like as
elaborate as yours with all the nested simulations and the like.

> the verifiable fact is that the input ⟨Ĥ⟩ ⟨Ĥ⟩ to Ĥ.qx is correctly
> decided as never halting.

(I'm going to ignore errors that I've already pointed out.)

> If you really do sincerely want an actual honest dialogue you would
> carefully work through all the steps to confirm that the input ⟨Ĥ⟩ ⟨Ĥ⟩
> to Ĥ.qx never halts.

If you want me to comment on that, write it without the errors. It has
two, both of which I've commented on before. If you are sincere, you
will want to write clearly and without errors.

> Once we have mutual agreement that Ĥ.qx correctly decides that its
> input: ⟨Ĥ⟩ ⟨Ĥ⟩ never halts and Ĥ does halt, then we have the basis to
> go to the next step and resolve the actual paradox.

There is no paradox. That Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qn when Ĥ applied to ⟨Ĥ⟩
clearly halts is not paradoxical. It's just not the sort of TM the
proof is talking about. And how could it be? The "Linz Ĥ" is as
illogical as a cat that is a dog.

> As long as it is simply dismissed out-of-hand as a contradiction the
> paradox remains unresolved.

There is no contradiction or paradox. You Ĥ is just the wrong sort of
TM. The proof you want to "refute" is talking about this sort of Ĥ:

Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qn
if (and only if) Ĥ applied to ⟨Ĥ⟩ does not halt.

--
Ben.

Re: Black box halt decider is NOT a partial decider [ Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] [ succinct ]

<NsudnY99rthDOJX8nZ2dnUU7-c_NnZ2d@giganews.com>

 copy mid

https://www.novabbs.com/devel/article-flat.php?id=19390&group=comp.theory#19390

 copy link   Newsgroups: comp.theory comp.ai.philosophy comp.software-eng sci.math.symbolic
Path: i2pn2.org!i2pn.org!weretis.net!feeder6.news.weretis.net!news.snarked.org!border2.nntp.dca1.giganews.com!nntp.giganews.com!buffer2.nntp.dca1.giganews.com!buffer1.nntp.dca1.giganews.com!news.giganews.com.POSTED!not-for-mail
NNTP-Posting-Date: Mon, 02 Aug 2021 21:11:42 -0500
Subject: Re:_Black_box_halt_decider_is_NOT_a_partial_decider_[
Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] [ succinct
]
Newsgroups: comp.theory,comp.ai.philosophy,comp.software-eng,sci.math.symbolic
References: <20210719214640.00000dfc@reddwarf.jmc> <871r7i6n2u.fsf@bsb.me.uk>
<OqKdnROLKJ9CdJz8nZ2dnUU7-avNnZ2d@giganews.com> <87k0la542c.fsf@bsb.me.uk>
<1NidnVPZ-NHDl5_8nZ2dnUU7-enNnZ2d@giganews.com> <87sfzw3ao1.fsf@bsb.me.uk>
<7oKdnTjx4IC20p78nZ2dnUU7-TvNnZ2d@giganews.com> <875yws36vt.fsf@bsb.me.uk>
<j66dnbdHrpV8_p78nZ2dnUU7-aXNnZ2d@giganews.com> <87im0s0ydp.fsf@bsb.me.uk>
<Brqdnfehrf0Kj5n8nZ2dnUU7-X3NnZ2d@giganews.com> <87tukblgjy.fsf@bsb.me.uk>
<qtGdnfuXs4nFOZn8nZ2dnUU7-cnNnZ2d@giganews.com> <871r7ekugt.fsf@bsb.me.uk>
<K5-dndGZo_-VmJv8nZ2dnUU78QvNnZ2d@giganews.com> <87czqxa0zk.fsf@bsb.me.uk>
<woudnXWBxPba95r8nZ2dnUU78ffNnZ2d@giganews.com> <87mtpz64sq.fsf@bsb.me.uk>
<w5edne8d06OkxpX8nZ2dnUU7-b_NnZ2d@giganews.com> <87bl6f5qvy.fsf@bsb.me.uk>
<xLednaPs_ZSXCZX8nZ2dnUU7-YnNnZ2d@giganews.com> <87o8af47y0.fsf@bsb.me.uk>
From: NoO...@NoWhere.com (olcott)
Date: Mon, 2 Aug 2021 21:11:41 -0500
User-Agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64; rv:78.0) Gecko/20100101
Thunderbird/78.12.0
MIME-Version: 1.0
In-Reply-To: <87o8af47y0.fsf@bsb.me.uk>
Content-Type: text/plain; charset=utf-8; format=flowed
Content-Language: en-US
Content-Transfer-Encoding: 8bit
Message-ID: <NsudnY99rthDOJX8nZ2dnUU7-c_NnZ2d@giganews.com>
Lines: 52
X-Usenet-Provider: http://www.giganews.com
X-Trace: sv3-gLMvEd4uUFe+Kc0LSP6oLaVjhpai56Q8fjajXZ2QGcEdbvPf4I2VoZyL8CVVSjmyRiBIaLiG1DIT9zP!svPKyruEZtNKdg8lhgQwW6z3/zu3oU7r/8mfn2Djl/fmtbi9BF1Z8/iFOoFcyaD6Tout9kxz5A==
X-Complaints-To: abuse@giganews.com
X-DMCA-Notifications: http://www.giganews.com/info/dmca.html
X-Abuse-and-DMCA-Info: Please be sure to forward a copy of ALL headers
X-Abuse-and-DMCA-Info: Otherwise we will be unable to process your complaint properly
X-Postfilter: 1.3.40
X-Original-Bytes: 4305
 by: olcott - Tue, 3 Aug 2021 02:11 UTC

On 8/2/2021 8:45 PM, Ben Bacarisse wrote:
> olcott <NoOne@NoWhere.com> writes:
>
>> On 8/2/2021 7:11 PM, Ben Bacarisse wrote:
>>> olcott <NoOne@NoWhere.com> writes:
>>>

> (I'm going to ignore errors that I've already pointed out.)
>
>> If you really do sincerely want an actual honest dialogue you would
>> carefully work through all the steps to confirm that the input ⟨Ĥ⟩ ⟨Ĥ⟩
>> to Ĥ.qx never halts.
>
> If you want me to comment on that, write it without the errors. It has
> two, both of which I've commented on before. If you are sincere, you
> will want to write clearly and without errors.
>
>> Once we have mutual agreement that Ĥ.qx correctly decides that its
>> input: ⟨Ĥ⟩ ⟨Ĥ⟩ never halts and Ĥ does halt, then we have the basis to
>> go to the next step and resolve the actual paradox.
>
> There is no paradox. That Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qn when Ĥ applied to ⟨Ĥ⟩
> clearly halts is not paradoxical. It's just not the sort of TM the
> proof is talking about. And how could it be? The "Linz Ĥ" is as
> illogical as a cat that is a dog.
>
>> As long as it is simply dismissed out-of-hand as a contradiction the
>> paradox remains unresolved.
>
> There is no contradiction or paradox. You Ĥ is just the wrong sort of
> TM. The proof you want to "refute" is talking about this sort of Ĥ:
>
> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qn
> if (and only if) Ĥ applied to ⟨Ĥ⟩ does not halt.
>

Ĥ.qx correctly decides that its input: ⟨Ĥ⟩ ⟨Ĥ⟩ never halts
Ĥ.qx correctly decides that its input: ⟨Ĥ⟩ ⟨Ĥ⟩ never halts
Ĥ.qx correctly decides that its input: ⟨Ĥ⟩ ⟨Ĥ⟩ never halts
Ĥ.qx correctly decides that its input: ⟨Ĥ⟩ ⟨Ĥ⟩ never halts

In computability theory, the halting problem is the problem of
determining, from a description of an arbitrary computer program and an
input, whether the program will finish running, or continue to run
forever https://en.wikipedia.org/wiki/Halting_problem

--
Copyright 2021 Pete Olcott

"Great spirits have always encountered violent opposition from mediocre
minds." Einstein

Pages:123456789101112131415161718192021
server_pubkey.txt

rocksolid light 0.9.7
clearnet tor