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devel / comp.theory / Re: Black box halt decider is NOT a partial decider

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

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Black box halt decider is NOT a partial decider

<20210719214640.00000dfc@reddwarf.jmc>

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From: flib...@reddwarf.jmc (Mr Flibble)
Newsgroups: comp.theory
Subject: Black box halt decider is NOT a partial decider
Message-ID: <20210719214640.00000dfc@reddwarf.jmc>
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 by: Mr Flibble - Mon, 19 Jul 2021 20:46 UTC

My black box halt decider is NOT a partial decider: it returns:

1) P halts
2) P does not halt
3) P is invalid

A halt / does not halt decision need not be reached for invalid
programs; they can simply be discarded as erroneous much like the
proofs based on the bullshit contradiction that makes those programs
erroneous.

/Flibble

Re: Black box halt decider is NOT a partial decider

<sd4pbc$f1b$1@gioia.aioe.org>

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From: chris.m....@gmail.com (Chris M. Thomasson)
Newsgroups: comp.theory
Subject: Re: Black box halt decider is NOT a partial decider
Date: Mon, 19 Jul 2021 14:03:40 -0700
Organization: Aioe.org NNTP Server
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 by: Chris M. Thomasson - Mon, 19 Jul 2021 21:03 UTC

On 7/19/2021 1:46 PM, Mr Flibble wrote:
> My black box halt decider is NOT a partial decider: it returns:
>
> 1) P halts
> 2) P does not halt
> 3) P is invalid
>
> A halt / does not halt decision need not be reached for invalid
> programs; they can simply be discarded as erroneous much like the
> proofs based on the bullshit contradiction that makes those programs
> erroneous.

What program is invalid?

Re: Black box halt decider is NOT a partial decider

<sd76r9$r63$3@dont-email.me>

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https://www.novabbs.com/devel/article-flat.php?id=18596&group=comp.theory#18596

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From: david.br...@hesbynett.no (David Brown)
Newsgroups: comp.theory
Subject: Re: Black box halt decider is NOT a partial decider
Date: Tue, 20 Jul 2021 21:06:17 +0200
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 by: David Brown - Tue, 20 Jul 2021 19:06 UTC

On 19/07/2021 23:03, Chris M. Thomasson wrote:
> On 7/19/2021 1:46 PM, Mr Flibble wrote:
>> My black box halt decider is NOT a partial decider: it returns:
>>
>> 1) P halts
>> 2) P does not halt
>> 3) P is invalid
>>
>> A halt / does not halt decision need not be reached for invalid
>> programs; they can simply be discarded as erroneous much like the
>> proofs based on the bullshit contradiction that makes those programs
>> erroneous.
>
> What program is invalid?

The ones for which the black box cannot guarantee a correct "halt" or
"does not halt" answer, obviously. That is, all but a small subset of
programs are invalid. Basically, his black box might be of some use for
testing a specific program or two.

Re: Black box halt decider is NOT a partial decider

<sd7cgs$1qmn$1@gioia.aioe.org>

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https://www.novabbs.com/devel/article-flat.php?id=18603&group=comp.theory#18603

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From: chris.m....@gmail.com (Chris M. Thomasson)
Newsgroups: comp.theory
Subject: Re: Black box halt decider is NOT a partial decider
Date: Tue, 20 Jul 2021 13:43:07 -0700
Organization: Aioe.org NNTP Server
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References: <20210719214640.00000dfc@reddwarf.jmc>
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 by: Chris M. Thomasson - Tue, 20 Jul 2021 20:43 UTC

On 7/20/2021 12:06 PM, David Brown wrote:
> On 19/07/2021 23:03, Chris M. Thomasson wrote:
>> On 7/19/2021 1:46 PM, Mr Flibble wrote:
>>> My black box halt decider is NOT a partial decider: it returns:
>>>
>>> 1) P halts
>>> 2) P does not halt
>>> 3) P is invalid
>>>
>>> A halt / does not halt decision need not be reached for invalid
>>> programs; they can simply be discarded as erroneous much like the
>>> proofs based on the bullshit contradiction that makes those programs
>>> erroneous.
>>
>> What program is invalid?
>
> The ones for which the black box cannot guarantee a correct "halt" or
> "does not halt" answer, obviously. That is, all but a small subset of
> programs are invalid. Basically, his black box might be of some use for
> testing a specific program or two.
>

Humm... I am thinking of a program that runs for a random amount of time
using a TRNG, then sends an email to its creator, a human. This person
reply's to the email either "continue", or "stop". If the program
receives "stop", it halts. Otherwise it runs for another random amount
of time, and sends another email...

Afaict, this is a legitimate program and is not invalid in any way,
shape or form. However, it would require the "black box" halting decider
to read the mind of the person who created the program. If the program
does not receive a response in say, 1 month, it runs again and sends
another email. Over and over again.

Re: Black box halt decider is NOT a partial decider

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Subject: Re: Black box halt decider is NOT a partial decider
Newsgroups: comp.theory
References: <20210719214640.00000dfc@reddwarf.jmc>
<sd4pbc$f1b$1@gioia.aioe.org> <sd76r9$r63$3@dont-email.me>
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From: Rich...@Damon-Family.org (Richard Damon)
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 by: Richard Damon - Tue, 20 Jul 2021 20:56 UTC

On 7/20/21 1:43 PM, Chris M. Thomasson wrote:
> On 7/20/2021 12:06 PM, David Brown wrote:
>> On 19/07/2021 23:03, Chris M. Thomasson wrote:
>>> On 7/19/2021 1:46 PM, Mr Flibble wrote:
>>>> My black box halt decider is NOT a partial decider: it returns:
>>>>
>>>> 1) P halts
>>>> 2) P does not halt
>>>> 3) P is invalid
>>>>
>>>> A halt / does not halt decision need not be reached for invalid
>>>> programs; they can simply be discarded as erroneous much like the
>>>> proofs based on the bullshit contradiction that makes those programs
>>>> erroneous.
>>>
>>> What program is invalid?
>>
>> The ones for which the black box cannot guarantee a correct "halt" or
>> "does not halt" answer, obviously.  That is, all but a small subset of
>> programs are invalid.  Basically, his black box might be of some use for
>> testing a specific program or two.
>>
>
> Humm... I am thinking of a program that runs for a random amount of time
> using a TRNG, then sends an email to its creator, a human. This person
> reply's to the email either "continue", or "stop". If the program
> receives "stop", it halts. Otherwise it runs for another random amount
> of time, and sends another email...
>
> Afaict, this is a legitimate program and is not invalid in any way,
> shape or form. However, it would require the "black box" halting decider
> to read the mind of the person who created the program. If the program
> does not receive a response in say, 1 month, it runs again and sends
> another email. Over and over again.

It may be a valid 'program' but doesn't meet the requirements for a
Turing Machine, and doesn't meet the requirements of a 'Computation'.

Thus the Halting Problem Theorem doesn't deal with this sort of thing.

This is perhaps one of the things that confuses some people, the Turing
Equivalence Theorem doesn't map all 'Programs' but all 'Computations',
with a fairly specific definition. One of the requirments for a
Computation is that all the input needs to be defined at the start, (or
at least all the data the program takes in is the 'input' that the
decider gets to see the copy of). As such, things like TRNG don't really
exist, but is just an input, that every run for the same 'computation'
needs to be the same.

Re: Black box halt decider is NOT a partial decider

<sd7eas$om3$1@dont-email.me>

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https://www.novabbs.com/devel/article-flat.php?id=18606&group=comp.theory#18606

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From: jbb...@notatt.com (Jeff Barnett)
Newsgroups: comp.theory
Subject: Re: Black box halt decider is NOT a partial decider
Date: Tue, 20 Jul 2021 15:14:01 -0600
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 by: Jeff Barnett - Tue, 20 Jul 2021 21:14 UTC

On 7/20/2021 2:43 PM, Chris M. Thomasson wrote:
> On 7/20/2021 12:06 PM, David Brown wrote:
>> On 19/07/2021 23:03, Chris M. Thomasson wrote:
>>> On 7/19/2021 1:46 PM, Mr Flibble wrote:
>>>> My black box halt decider is NOT a partial decider: it returns:
>>>>
>>>> 1) P halts
>>>> 2) P does not halt
>>>> 3) P is invalid
>>>>
>>>> A halt / does not halt decision need not be reached for invalid
>>>> programs; they can simply be discarded as erroneous much like the
>>>> proofs based on the bullshit contradiction that makes those programs
>>>> erroneous.
>>>
>>> What program is invalid?
>>
>> The ones for which the black box cannot guarantee a correct "halt" or
>> "does not halt" answer, obviously.  That is, all but a small subset of
>> programs are invalid.  Basically, his black box might be of some use for
>> testing a specific program or two.
>>
>
> Humm... I am thinking of a program that runs for a random amount of time
> using a TRNG, then sends an email to its creator, a human. This person
> reply's to the email either "continue", or "stop". If the program
> receives "stop", it halts. Otherwise it runs for another random amount
> of time, and sends another email...
>
> Afaict, this is a legitimate program and is not invalid in any way,
> shape or form. However, it would require the "black box" halting decider
> to read the mind of the person who created the program. If the program
> does not receive a response in say, 1 month, it runs again and sends
> another email. Over and over again.

A TM either implements a partial or a total function. Your example is
neither; it's a hodge podge.

If you want to reason about a probabilistic TM, chose a model (there are
several). Now state a halting theorem for your model of choice, get
busy, and do some mathematics. You are not allowed to change the model
under discussion and act like nothing else is change; that's a PO move
and to be avoided.
--
Jeff Barnett

Re: Black box halt decider is NOT a partial decider

<sd7een$js8$1@gioia.aioe.org>

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https://www.novabbs.com/devel/article-flat.php?id=18607&group=comp.theory#18607

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From: chris.m....@gmail.com (Chris M. Thomasson)
Newsgroups: comp.theory
Subject: Re: Black box halt decider is NOT a partial decider
Date: Tue, 20 Jul 2021 14:16:05 -0700
Organization: Aioe.org NNTP Server
Message-ID: <sd7een$js8$1@gioia.aioe.org>
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 by: Chris M. Thomasson - Tue, 20 Jul 2021 21:16 UTC

On 7/20/2021 1:56 PM, Richard Damon wrote:
> On 7/20/21 1:43 PM, Chris M. Thomasson wrote:
>> On 7/20/2021 12:06 PM, David Brown wrote:
>>> On 19/07/2021 23:03, Chris M. Thomasson wrote:
>>>> On 7/19/2021 1:46 PM, Mr Flibble wrote:
>>>>> My black box halt decider is NOT a partial decider: it returns:
>>>>>
>>>>> 1) P halts
>>>>> 2) P does not halt
>>>>> 3) P is invalid
>>>>>
>>>>> A halt / does not halt decision need not be reached for invalid
>>>>> programs; they can simply be discarded as erroneous much like the
>>>>> proofs based on the bullshit contradiction that makes those programs
>>>>> erroneous.
>>>>
>>>> What program is invalid?
>>>
>>> The ones for which the black box cannot guarantee a correct "halt" or
>>> "does not halt" answer, obviously.  That is, all but a small subset of
>>> programs are invalid.  Basically, his black box might be of some use for
>>> testing a specific program or two.
>>>
>>
>> Humm... I am thinking of a program that runs for a random amount of time
>> using a TRNG, then sends an email to its creator, a human. This person
>> reply's to the email either "continue", or "stop". If the program
>> receives "stop", it halts. Otherwise it runs for another random amount
>> of time, and sends another email...
>>
>> Afaict, this is a legitimate program and is not invalid in any way,
>> shape or form. However, it would require the "black box" halting decider
>> to read the mind of the person who created the program. If the program
>> does not receive a response in say, 1 month, it runs again and sends
>> another email. Over and over again.
>
> It may be a valid 'program' but doesn't meet the requirements for a
> Turing Machine, and doesn't meet the requirements of a 'Computation'.
>
> Thus the Halting Problem Theorem doesn't deal with this sort of thing.
>
> This is perhaps one of the things that confuses some people,

Indeed. I got confused and thought that a universal halting decider can
work with any arbitrary program.

> the Turing
> Equivalence Theorem doesn't map all 'Programs' but all 'Computations',
> with a fairly specific definition. One of the requirments for a
> Computation is that all the input needs to be defined at the start, (or
> at least all the data the program takes in is the 'input' that the
> decider gets to see the copy of). As such, things like TRNG don't really
> exist, but is just an input, that every run for the same 'computation'
> needs to be the same.
>

Now I am thinking of a "special" Turing machine with an internal coin it
can flip. If the machine reads a certain instruction, it flips its coin
and uses the result, either a 0 or a 1, as if it just read it from the
tape. The internal coin can be physically flipped with a mechanical
device or something. lol. I hope that does not stick me directly in the
center of Kookville. Yikes!

;^o

Re: Black box halt decider is NOT a partial decider

<sd7eho$js8$2@gioia.aioe.org>

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https://www.novabbs.com/devel/article-flat.php?id=18608&group=comp.theory#18608

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From: chris.m....@gmail.com (Chris M. Thomasson)
Newsgroups: comp.theory
Subject: Re: Black box halt decider is NOT a partial decider
Date: Tue, 20 Jul 2021 14:17:43 -0700
Organization: Aioe.org NNTP Server
Message-ID: <sd7eho$js8$2@gioia.aioe.org>
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 by: Chris M. Thomasson - Tue, 20 Jul 2021 21:17 UTC

On 7/20/2021 2:14 PM, Jeff Barnett wrote:
> On 7/20/2021 2:43 PM, Chris M. Thomasson wrote:
>> On 7/20/2021 12:06 PM, David Brown wrote:
>>> On 19/07/2021 23:03, Chris M. Thomasson wrote:
>>>> On 7/19/2021 1:46 PM, Mr Flibble wrote:
>>>>> My black box halt decider is NOT a partial decider: it returns:
>>>>>
>>>>> 1) P halts
>>>>> 2) P does not halt
>>>>> 3) P is invalid
>>>>>
>>>>> A halt / does not halt decision need not be reached for invalid
>>>>> programs; they can simply be discarded as erroneous much like the
>>>>> proofs based on the bullshit contradiction that makes those programs
>>>>> erroneous.
>>>>
>>>> What program is invalid?
>>>
>>> The ones for which the black box cannot guarantee a correct "halt" or
>>> "does not halt" answer, obviously.  That is, all but a small subset of
>>> programs are invalid.  Basically, his black box might be of some use for
>>> testing a specific program or two.
>>>
>>
>> Humm... I am thinking of a program that runs for a random amount of
>> time using a TRNG, then sends an email to its creator, a human. This
>> person reply's to the email either "continue", or "stop". If the
>> program receives "stop", it halts. Otherwise it runs for another
>> random amount of time, and sends another email...
>>
>> Afaict, this is a legitimate program and is not invalid in any way,
>> shape or form. However, it would require the "black box" halting
>> decider to read the mind of the person who created the program. If the
>> program does not receive a response in say, 1 month, it runs again and
>> sends another email. Over and over again.
>
> A TM either implements a partial or a total function. Your example is
> neither; it's a hodge podge.
>
> If you want to reason about a probabilistic TM, chose a model (there are
> several). Now state a halting theorem for your model of choice, get
> busy, and do some mathematics. You are not allowed to change the model
> under discussion and act like nothing else is change; that's a PO move
> and to be avoided.

Yeah. Sorry, I had some sort of universal halt decider on the mind that
can work with any x86 program. ;^(

Re: Black box halt decider is NOT a partial decider

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https://www.novabbs.com/devel/article-flat.php?id=18609&group=comp.theory#18609

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Subject: Re: Black box halt decider is NOT a partial decider
Newsgroups: comp.theory
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From: Rich...@Damon-Family.org (Richard Damon)
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 by: Richard Damon - Tue, 20 Jul 2021 21:50 UTC

On 7/20/21 2:16 PM, Chris M. Thomasson wrote:
> On 7/20/2021 1:56 PM, Richard Damon wrote:
>> On 7/20/21 1:43 PM, Chris M. Thomasson wrote:
>>> On 7/20/2021 12:06 PM, David Brown wrote:
>>>> On 19/07/2021 23:03, Chris M. Thomasson wrote:
>>>>> On 7/19/2021 1:46 PM, Mr Flibble wrote:
>>>>>> My black box halt decider is NOT a partial decider: it returns:
>>>>>>
>>>>>> 1) P halts
>>>>>> 2) P does not halt
>>>>>> 3) P is invalid
>>>>>>
>>>>>> A halt / does not halt decision need not be reached for invalid
>>>>>> programs; they can simply be discarded as erroneous much like the
>>>>>> proofs based on the bullshit contradiction that makes those programs
>>>>>> erroneous.
>>>>>
>>>>> What program is invalid?
>>>>
>>>> The ones for which the black box cannot guarantee a correct "halt" or
>>>> "does not halt" answer, obviously.  That is, all but a small subset of
>>>> programs are invalid.  Basically, his black box might be of some use
>>>> for
>>>> testing a specific program or two.
>>>>
>>>
>>> Humm... I am thinking of a program that runs for a random amount of time
>>> using a TRNG, then sends an email to its creator, a human. This person
>>> reply's to the email either "continue", or "stop". If the program
>>> receives "stop", it halts. Otherwise it runs for another random amount
>>> of time, and sends another email...
>>>
>>> Afaict, this is a legitimate program and is not invalid in any way,
>>> shape or form. However, it would require the "black box" halting decider
>>> to read the mind of the person who created the program. If the program
>>> does not receive a response in say, 1 month, it runs again and sends
>>> another email. Over and over again.
>>
>> It may be a valid 'program' but doesn't meet the requirements for a
>> Turing Machine, and doesn't meet the requirements of a 'Computation'.
>>
>> Thus the Halting Problem Theorem doesn't deal with this sort of thing.
>>
>> This is perhaps one of the things that confuses some people,
>
> Indeed. I got confused and thought that a universal halting decider can
> work with any arbitrary program.
>
>
>> the Turing
>> Equivalence Theorem doesn't map all 'Programs' but all 'Computations',
>> with a fairly specific definition. One of the requirments for a
>> Computation is that all the input needs to be defined at the start, (or
>> at least all the data the program takes in is the 'input' that the
>> decider gets to see the copy of). As such, things like TRNG don't really
>> exist, but is just an input, that every run for the same 'computation'
>> needs to be the same.
>>
>
> Now I am thinking of a "special" Turing machine with an internal coin it
> can flip. If the machine reads a certain instruction, it flips its coin
> and uses the result, either a 0 or a 1, as if it just read it from the
> tape. The internal coin can be physically flipped with a mechanical
> device or something. lol. I hope that does not stick me directly in the
> center of Kookville. Yikes!
>
> ;^o

The problem is that Turing Machines are precisely defined for a purpose.
and 'randomness' isn't part of that major purpose.

Yes, there are variations that that can do some randomness, but I am not
sure how much things like the Halting Theorem apply, after all, if a
machine can act differently on different runs, can you really try to
predict what it will do?

Re: Black box halt decider is NOT a partial decider

<sd8bim$1set$1@gioia.aioe.org>

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From: chris.m....@gmail.com (Chris M. Thomasson)
Newsgroups: comp.theory
Subject: Re: Black box halt decider is NOT a partial decider
Date: Tue, 20 Jul 2021 22:33:08 -0700
Organization: Aioe.org NNTP Server
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 by: Chris M. Thomasson - Wed, 21 Jul 2021 05:33 UTC

On 7/20/2021 2:50 PM, Richard Damon wrote:
> On 7/20/21 2:16 PM, Chris M. Thomasson wrote:
>> On 7/20/2021 1:56 PM, Richard Damon wrote:
>>> On 7/20/21 1:43 PM, Chris M. Thomasson wrote:
>>>> On 7/20/2021 12:06 PM, David Brown wrote:
>>>>> On 19/07/2021 23:03, Chris M. Thomasson wrote:
>>>>>> On 7/19/2021 1:46 PM, Mr Flibble wrote:
>>>>>>> My black box halt decider is NOT a partial decider: it returns:
[...]
>> Now I am thinking of a "special" Turing machine with an internal coin it
>> can flip. If the machine reads a certain instruction, it flips its coin
>> and uses the result, either a 0 or a 1, as if it just read it from the
>> tape. The internal coin can be physically flipped with a mechanical
>> device or something. lol. I hope that does not stick me directly in the
>> center of Kookville. Yikes!
>>
>> ;^o
>
> The problem is that Turing Machines are precisely defined for a purpose.
> and 'randomness' isn't part of that major purpose.
>
> Yes, there are variations that that can do some randomness, but I am not
> sure how much things like the Halting Theorem apply, after all, if a
> machine can act differently on different runs, can you really try to
> predict what it will do?
>

For some stupid reason I always thought that the halting problem extends
to all problems, and all programs. If the program is random in nature,
and can halt from time to time, or never halt at all, well... This so
called "decider" of the halting problem would be able to determine its
ultimate fate, so to speak...

Well, here is some pure sarcasm:

Every program halts because they will not get to run forever...
Eventually, Earth will die. So will the computers running programs when
a meteor hits, or the sun dies. ahhh, but what about infinity? lol. For
some reason, it makes me think of the follow clip from the Neverending
Story:

https://youtu.be/5sEZmMeH96Q

;^o

Re: Black box halt decider is NOT a partial decider

<J9PJI.14573$6U5.3457@fx02.iad>

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Subject: Re: Black box halt decider is NOT a partial decider
Newsgroups: comp.theory
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From: Rich...@Damon-Family.org (Richard Damon)
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 by: Richard Damon - Wed, 21 Jul 2021 06:30 UTC

On 7/20/21 10:33 PM, Chris M. Thomasson wrote:
> On 7/20/2021 2:50 PM, Richard Damon wrote:
>> On 7/20/21 2:16 PM, Chris M. Thomasson wrote:
>>> On 7/20/2021 1:56 PM, Richard Damon wrote:
>>>> On 7/20/21 1:43 PM, Chris M. Thomasson wrote:
>>>>> On 7/20/2021 12:06 PM, David Brown wrote:
>>>>>> On 19/07/2021 23:03, Chris M. Thomasson wrote:
>>>>>>> On 7/19/2021 1:46 PM, Mr Flibble wrote:
>>>>>>>> My black box halt decider is NOT a partial decider: it returns:
> [...]
>>> Now I am thinking of a "special" Turing machine with an internal coin it
>>> can flip. If the machine reads a certain instruction, it flips its coin
>>> and uses the result, either a 0 or a 1, as if it just read it from the
>>> tape. The internal coin can be physically flipped with a mechanical
>>> device or something. lol. I hope that does not stick me directly in the
>>> center of Kookville. Yikes!
>>>
>>> ;^o
>>
>> The problem is that Turing Machines are precisely defined for a purpose.
>> and 'randomness' isn't part of that major purpose.
>>
>> Yes, there are variations that that can do some randomness, but I am not
>> sure how much things like the Halting Theorem apply, after all, if a
>> machine can act differently on different runs, can you really try to
>> predict what it will do?
>>
>
> For some stupid reason I always thought that the halting problem extends
> to all problems, and all programs. If the program is random in nature,
> and can halt from time to time, or never halt at all, well... This so
> called "decider" of the halting problem would be able to determine its
> ultimate fate, so to speak...
>
> Well, here is some pure sarcasm:
>
> Every program halts because they will not get to run forever...
> Eventually, Earth will die. So will the computers running programs when
> a meteor hits, or the sun dies. ahhh, but what about infinity? lol. For
> some reason, it makes me think of the follow clip from the Neverending
> Story:
>
> https://youtu.be/5sEZmMeH96Q
>
> ;^o

Well, at least the Halting problem that we have been describing is about
Turing Machines, and Turing Machines are theoretical machines, and not
actually dependent on the physical universe, but only on Mathematical
logic.

Halting isn't just not running anymore because the 'machine' that is
running it has broken, but is actually reaching a designated 'halt'
state. It is possible to 'design' a halting calculation that would never
halt in the lifetime of the universe, because the number of steps it
needs to reach that final state exceeds the finite number of time
quantum in the expected lifespan of the universe (and maybe uses more
storage than particles in the universe). But this is still considered a
'Halting' computation, as theoretically we know that it WILL get then in
a finite (but stupidly large) number of steps.

Dispite what we might think of the name, Computation Theory isn't really
about what we think about as a 'Computer' but the fundamental
mathematical concept of a 'Computation' which computes some result using
finite mechanical operations.

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From: ben.use...@bsb.me.uk (Ben Bacarisse)
Newsgroups: comp.theory
Subject: Re: Black box halt decider is NOT a partial decider
Date: Wed, 21 Jul 2021 13:17:53 +0100
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 by: Ben Bacarisse - Wed, 21 Jul 2021 12:17 UTC

"Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> writes:

> For some stupid reason I always thought that the halting problem
> extends to all problems, and all programs.

It is a problem in mathematics and, like all mathematics, it is based on
sound definitions. It says nothing about "all programs" unless "all
programs" is a well-specified set. In that case, "all programs" might
well have a halting problem, and might even have a halting theorem.

The problem is always grounded to the context of some formal model of
computation like Turing machines, recursive functions or the lambda
calculus. I say "always" but that has to exclude comp.theory which is
dominated by silly ideas coming from people who don't know much about
such format models.

> Well, here is some pure sarcasm:
>
> Every program halts because they will not get to run
> forever... Eventually, Earth will die.

This is not just sarcasm. It's a plain fact.

--
Ben.

Re: Black box halt decider is NOT a partial decider

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Subject: Re: Black box halt decider is NOT a partial decider
From: malcolm....@gmail.com (Malcolm McLean)
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 by: Malcolm McLean - Wed, 21 Jul 2021 12:46 UTC

On Wednesday, 21 July 2021 at 06:33:13 UTC+1, Chris M. Thomasson wrote:
> On 7/20/2021 2:50 PM, Richard Damon wrote:
>
> > Yes, there are variations that that can do some randomness, but I am not
> > sure how much things like the Halting Theorem apply, after all, if a
> > machine can act differently on different runs, can you really try to
> > predict what it will do?
> >
> For some stupid reason I always thought that the halting problem extends
> to all problems, and all programs. If the program is random in nature,
> and can halt from time to time, or never halt at all, well... This so
> called "decider" of the halting problem would be able to determine its
> ultimate fate, so to speak...
>
We could implement randomness by providing the Turing machine
with a set of random numbers for its tape. The set can't be infinite
for the "Linz" proof to work, otherwise the copy loop never halts.
But Turing machines can't contain random number generators. Any
physical machine will of course have a slight chance of malfunctiing,
introducing randomness in a sense. But the mathematical model excludes
that possibility.

Most computers are sufficiently close to Turing machines for Turing machine
concepts to be extensible to them. But not always. "Eliza" can't really
be analysed that way, for example. (It's a fake psychotherapist that works by
recognising a few grammar words and then throwing the open class words back
at you).

Re: Black box halt decider is NOT a partial decider

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From: ben.use...@bsb.me.uk (Ben Bacarisse)
Newsgroups: comp.theory
Subject: Re: Black box halt decider is NOT a partial decider
Date: Wed, 21 Jul 2021 14:12:56 +0100
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 by: Ben Bacarisse - Wed, 21 Jul 2021 13:12 UTC

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

> On Wednesday, 21 July 2021 at 06:33:13 UTC+1, Chris M. Thomasson wrote:
>> On 7/20/2021 2:50 PM, Richard Damon wrote:
>>
>> > Yes, there are variations that that can do some randomness, but I am not
>> > sure how much things like the Halting Theorem apply, after all, if a
>> > machine can act differently on different runs, can you really try to
>> > predict what it will do?
>> >
>> For some stupid reason I always thought that the halting problem extends
>> to all problems, and all programs. If the program is random in nature,
>> and can halt from time to time, or never halt at all, well... This so
>> called "decider" of the halting problem would be able to determine its
>> ultimate fate, so to speak...
>>
> We could implement randomness by providing the Turing machine
> with a set of random numbers for its tape. The set can't be infinite
> for the "Linz" proof to work, otherwise the copy loop never halts.

There are well-studied variations of Turing machines with stochastic
behaviour. None of the ones I've seen would prevent copying of the
input tape.

> But Turing machines can't contain random number generators. Any
> physical machine will of course have a slight chance of malfunctiing,
> introducing randomness in a sense. But the mathematical model excludes
> that possibility.

Why do you say that? Mathematical models of computation don't really
exclude anything, provided it can be properly specified.

--
Ben.

Re: Black box halt decider is NOT a partial decider

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Subject: Re: Black box halt decider is NOT a partial decider
From: malcolm....@gmail.com (Malcolm McLean)
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 by: Malcolm McLean - Wed, 21 Jul 2021 13:27 UTC

On Wednesday, 21 July 2021 at 14:12:58 UTC+1, Ben Bacarisse wrote:
> Malcolm McLean <malcolm.ar...@gmail.com> writes:
>
> > On Wednesday, 21 July 2021 at 06:33:13 UTC+1, Chris M. Thomasson wrote:
> >> On 7/20/2021 2:50 PM, Richard Damon wrote:
> >>
> >> > Yes, there are variations that that can do some randomness, but I am not
> >> > sure how much things like the Halting Theorem apply, after all, if a
> >> > machine can act differently on different runs, can you really try to
> >> > predict what it will do?
> >> >
> >> For some stupid reason I always thought that the halting problem extends
> >> to all problems, and all programs. If the program is random in nature,
> >> and can halt from time to time, or never halt at all, well... This so
> >> called "decider" of the halting problem would be able to determine its
> >> ultimate fate, so to speak...
> >>
> > We could implement randomness by providing the Turing machine
> > with a set of random numbers for its tape. The set can't be infinite
> > for the "Linz" proof to work, otherwise the copy loop never halts.
> There are well-studied variations of Turing machines with stochastic
> behaviour. None of the ones I've seen would prevent copying of the
> input tape.
>
You can implement a stochastic machine (if I understand you correctly)
by having a conventional machine and a list of random numbers on the tape.
If it encounters an instruction such as "move head left / right with 50%
probability" it reads a random number.
However the list of random numbers can't be infinite if you want to copy
the input tape.
>
> > But Turing machines can't contain random number generators. Any
> > physical machine will of course have a slight chance of malfunctiing,
> > introducing randomness in a sense. But the mathematical model excludes
> > that possibility.
> Why do you say that? Mathematical models of computation don't really
> exclude anything, provided it can be properly specified.
>
__The mathematical model__ Of course another mathematical model could
include randomness. We model noise all the time in biochemistry (it's
fundamental to how things work at the big molecule scale).

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Subject: Re: Black box halt decider is NOT a partial decider
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 by: Ben Bacarisse - Wed, 21 Jul 2021 15:28 UTC

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

> On Wednesday, 21 July 2021 at 14:12:58 UTC+1, Ben Bacarisse wrote:
>> Malcolm McLean <malcolm.ar...@gmail.com> writes:
>>
>> > On Wednesday, 21 July 2021 at 06:33:13 UTC+1, Chris M. Thomasson wrote:
>> >> On 7/20/2021 2:50 PM, Richard Damon wrote:
>> >>
>> >> > Yes, there are variations that that can do some randomness, but I am not
>> >> > sure how much things like the Halting Theorem apply, after all, if a
>> >> > machine can act differently on different runs, can you really try to
>> >> > predict what it will do?
>> >> >
>> >> For some stupid reason I always thought that the halting problem extends
>> >> to all problems, and all programs. If the program is random in nature,
>> >> and can halt from time to time, or never halt at all, well... This so
>> >> called "decider" of the halting problem would be able to determine its
>> >> ultimate fate, so to speak...
>> >>
>> > We could implement randomness by providing the Turing machine
>> > with a set of random numbers for its tape. The set can't be infinite
>> > for the "Linz" proof to work, otherwise the copy loop never halts.
>> There are well-studied variations of Turing machines with stochastic
>> behaviour. None of the ones I've seen would prevent copying of the
>> input tape.
>>
> You can implement a stochastic machine (if I understand you correctly)
> by having a conventional machine and a list of random numbers on the tape.
> If it encounters an instruction such as "move head left / right with 50%
> probability" it reads a random number.
> However the list of random numbers can't be infinite if you want to copy
> the input tape.

That's not how it's done. There are several such models, but in the one
with random content on a tape, that tape is not considered input. If it
were, the behaviour would be entirely determined by the input. It's
usual that the random tape is considered to be unbounded.

--
Ben.

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From: chris.m....@gmail.com (Chris M. Thomasson)
Newsgroups: comp.theory
Subject: Re: Black box halt decider is NOT a partial decider
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 by: Chris M. Thomasson - Thu, 22 Jul 2021 20:35 UTC

On 7/21/2021 5:17 AM, Ben Bacarisse wrote:
> "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> writes:
>
>> For some stupid reason I always thought that the halting problem
>> extends to all problems, and all programs.
>
> It is a problem in mathematics and, like all mathematics, it is based on
> sound definitions. It says nothing about "all programs" unless "all
> programs" is a well-specified set. In that case, "all programs" might
> well have a halting problem, and might even have a halting theorem.
>
> The problem is always grounded to the context of some formal model of
> computation like Turing machines, recursive functions or the lambda
> calculus. I say "always" but that has to exclude comp.theory which is
> dominated by silly ideas coming from people who don't know much about
> such format models.
>
>> Well, here is some pure sarcasm:
>>
>> Every program halts because they will not get to run
>> forever... Eventually, Earth will die.
>
> This is not just sarcasm. It's a plain fact.
>

Well, based on this fact, can we say everything on Earth halts because
the planet will eventually die?

Humm... It should be "helpful" to think about infinity, where the
program is being executed on a system that never dies. Its output is
being observed by beings that never die.

Does the program halt in the realm of the infinite?

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 by: Ben Bacarisse - Thu, 22 Jul 2021 21:10 UTC

"Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> writes:

> On 7/21/2021 5:17 AM, Ben Bacarisse wrote:
>> "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> writes:
>>
>>> For some stupid reason I always thought that the halting problem
>>> extends to all problems, and all programs.
>> It is a problem in mathematics and, like all mathematics, it is based on
>> sound definitions. It says nothing about "all programs" unless "all
>> programs" is a well-specified set. In that case, "all programs" might
>> well have a halting problem, and might even have a halting theorem.
>> The problem is always grounded to the context of some formal model of
>> computation like Turing machines, recursive functions or the lambda
>> calculus. I say "always" but that has to exclude comp.theory which is
>> dominated by silly ideas coming from people who don't know much about
>> such format models.
>>
>>> Well, here is some pure sarcasm:
>>>
>>> Every program halts because they will not get to run
>>> forever... Eventually, Earth will die.
>> This is not just sarcasm. It's a plain fact.
>>
>
> Well, based on this fact, can we say everything on Earth halts because
> the planet will eventually die?
>
> Humm... It should be "helpful" to think about infinity, where the
> program is being executed on a system that never dies. Its output is
> being observed by beings that never die.
>
> Does the program halt in the realm of the infinite?

I don't know what this means. I can answer about the mathematics, but I
don't know about these hypothetical computations that take time and are
"observed" by mythical creatures.

--
Ben.

Re: Black box halt decider is NOT a partial decider

<cMlKI.54700$h8.48024@fx47.iad>

 copy mid

https://www.novabbs.com/devel/article-flat.php?id=18765&group=comp.theory#18765

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Subject: Re: Black box halt decider is NOT a partial decider
Newsgroups: comp.theory
References: <20210719214640.00000dfc@reddwarf.jmc>
<sd4pbc$f1b$1@gioia.aioe.org> <sd76r9$r63$3@dont-email.me>
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From: Rich...@Damon-Family.org (Richard Damon)
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 by: Richard Damon - Thu, 22 Jul 2021 21:52 UTC

On 7/22/21 1:35 PM, Chris M. Thomasson wrote:
> On 7/21/2021 5:17 AM, Ben Bacarisse wrote:
>> "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> writes:
>>
>>> For some stupid reason I always thought that the halting problem
>>> extends to all problems, and all programs.
>>
>> It is a problem in mathematics and, like all mathematics, it is based on
>> sound definitions.  It says nothing about "all programs" unless "all
>> programs" is a well-specified set.  In that case, "all programs" might
>> well have a halting problem, and might even have a halting theorem.
>>
>> The problem is always grounded to the context of some formal model of
>> computation like Turing machines, recursive functions or the lambda
>> calculus.  I say "always" but that has to exclude comp.theory which is
>> dominated by silly ideas coming from people who don't know much about
>> such format models.
>>
>>> Well, here is some pure sarcasm:
>>>
>>> Every program halts because they will not get to run
>>> forever... Eventually, Earth will die.
>>
>> This is not just sarcasm.  It's a plain fact.
>>
>
> Well, based on this fact, can we say everything on Earth halts because
> the planet will eventually die?
>
> Humm... It should be "helpful" to think about infinity, where the
> program is being executed on a system that never dies. Its output is
> being observed by beings that never die.
>
> Does the program halt in the realm of the infinite?

The ACTUAL question for Computation Theory is does the Comutation reach
the Halt state in a FINITE number of steps.

If the Computation would reach the Halt State, but only after an
Infinite Number of Steps (even if 'just' a countably infinite number of
steps) it is called Non-Halting.

That is the FIRM dividing line. Is the number of steps needed to get the
answer a member of the Counting Numbers N.

I suppose some other realm might be developed that allow for an
'infinite' number of steps, but that starts to get a bit harder to define.

Re: Black box halt decider is NOT a partial decider

<sdfbrq$14bi$1@gioia.aioe.org>

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https://www.novabbs.com/devel/article-flat.php?id=18801&group=comp.theory#18801

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From: chris.m....@gmail.com (Chris M. Thomasson)
Newsgroups: comp.theory
Subject: Re: Black box halt decider is NOT a partial decider
Date: Fri, 23 Jul 2021 14:20:56 -0700
Organization: Aioe.org NNTP Server
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 by: Chris M. Thomasson - Fri, 23 Jul 2021 21:20 UTC

On 7/22/2021 2:52 PM, Richard Damon wrote:
> On 7/22/21 1:35 PM, Chris M. Thomasson wrote:
>> On 7/21/2021 5:17 AM, Ben Bacarisse wrote:
>>> "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> writes:
>>>
>>>> For some stupid reason I always thought that the halting problem
>>>> extends to all problems, and all programs.
>>>
>>> It is a problem in mathematics and, like all mathematics, it is based on
>>> sound definitions.  It says nothing about "all programs" unless "all
>>> programs" is a well-specified set.  In that case, "all programs" might
>>> well have a halting problem, and might even have a halting theorem.
>>>
>>> The problem is always grounded to the context of some formal model of
>>> computation like Turing machines, recursive functions or the lambda
>>> calculus.  I say "always" but that has to exclude comp.theory which is
>>> dominated by silly ideas coming from people who don't know much about
>>> such format models.
>>>
>>>> Well, here is some pure sarcasm:
>>>>
>>>> Every program halts because they will not get to run
>>>> forever... Eventually, Earth will die.
>>>
>>> This is not just sarcasm.  It's a plain fact.
>>>
>>
>> Well, based on this fact, can we say everything on Earth halts because
>> the planet will eventually die?
>>
>> Humm... It should be "helpful" to think about infinity, where the
>> program is being executed on a system that never dies. Its output is
>> being observed by beings that never die.
>>
>> Does the program halt in the realm of the infinite?
>
> The ACTUAL question for Computation Theory is does the Comutation reach
> the Halt state in a FINITE number of steps.

Theoretically, what if the program does halt in a FINITE number of steps
but it would take so long that the Earth would be dead by then. How can
the halt decider determine that?

>
> If the Computation would reach the Halt State, but only after an
> Infinite Number of Steps (even if 'just' a countably infinite number of
> steps) it is called Non-Halting.
>
> That is the FIRM dividing line. Is the number of steps needed to get the
> answer a member of the Counting Numbers N.
>
> I suppose some other realm might be developed that allow for an
> 'infinite' number of steps, but that starts to get a bit harder to define.
>

Re: Black box halt decider is NOT a partial decider

<sdfbv2$14bi$2@gioia.aioe.org>

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https://www.novabbs.com/devel/article-flat.php?id=18802&group=comp.theory#18802

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From: chris.m....@gmail.com (Chris M. Thomasson)
Newsgroups: comp.theory
Subject: Re: Black box halt decider is NOT a partial decider
Date: Fri, 23 Jul 2021 14:22:41 -0700
Organization: Aioe.org NNTP Server
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 by: Chris M. Thomasson - Fri, 23 Jul 2021 21:22 UTC

On 7/22/2021 2:10 PM, Ben Bacarisse wrote:
> "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> writes:
>
>> On 7/21/2021 5:17 AM, Ben Bacarisse wrote:
>>> "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> writes:
>>>
>>>> For some stupid reason I always thought that the halting problem
>>>> extends to all problems, and all programs.
>>> It is a problem in mathematics and, like all mathematics, it is based on
>>> sound definitions. It says nothing about "all programs" unless "all
>>> programs" is a well-specified set. In that case, "all programs" might
>>> well have a halting problem, and might even have a halting theorem.
>>> The problem is always grounded to the context of some formal model of
>>> computation like Turing machines, recursive functions or the lambda
>>> calculus. I say "always" but that has to exclude comp.theory which is
>>> dominated by silly ideas coming from people who don't know much about
>>> such format models.
>>>
>>>> Well, here is some pure sarcasm:
>>>>
>>>> Every program halts because they will not get to run
>>>> forever... Eventually, Earth will die.
>>> This is not just sarcasm. It's a plain fact.
>>>
>>
>> Well, based on this fact, can we say everything on Earth halts because
>> the planet will eventually die?
>>
>> Humm... It should be "helpful" to think about infinity, where the
>> program is being executed on a system that never dies. Its output is
>> being observed by beings that never die.
>>
>> Does the program halt in the realm of the infinite?
>
> I don't know what this means. I can answer about the mathematics, but I
> don't know about these hypothetical computations that take time and are
> "observed" by mythical creatures.
>

I was just wondering if the algorihtm might halt in a finite number of
steps, but the number of steps would take a very long time. The Earth
would be dead long before it gets a chance to halt. Does that make any
sense at all? Humm...

Re: Black box halt decider is NOT a partial decider

<ZxGKI.74701$VU3.61668@fx46.iad>

 copy mid

https://www.novabbs.com/devel/article-flat.php?id=18804&group=comp.theory#18804

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Subject: Re: Black box halt decider is NOT a partial decider
Newsgroups: comp.theory
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From: Rich...@Damon-Family.org (Richard Damon)
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 by: Richard Damon - Fri, 23 Jul 2021 21:30 UTC

On 7/23/21 2:22 PM, Chris M. Thomasson wrote:
> On 7/22/2021 2:10 PM, Ben Bacarisse wrote:
>> "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> writes:
>>
>>> On 7/21/2021 5:17 AM, Ben Bacarisse wrote:
>>>> "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> writes:
>>>>
>>>>> For some stupid reason I always thought that the halting problem
>>>>> extends to all problems, and all programs.
>>>> It is a problem in mathematics and, like all mathematics, it is
>>>> based on
>>>> sound definitions.  It says nothing about "all programs" unless "all
>>>> programs" is a well-specified set.  In that case, "all programs" might
>>>> well have a halting problem, and might even have a halting theorem.
>>>> The problem is always grounded to the context of some formal model of
>>>> computation like Turing machines, recursive functions or the lambda
>>>> calculus.  I say "always" but that has to exclude comp.theory which is
>>>> dominated by silly ideas coming from people who don't know much about
>>>> such format models.
>>>>
>>>>> Well, here is some pure sarcasm:
>>>>>
>>>>> Every program halts because they will not get to run
>>>>> forever... Eventually, Earth will die.
>>>> This is not just sarcasm.  It's a plain fact.
>>>>
>>>
>>> Well, based on this fact, can we say everything on Earth halts because
>>> the planet will eventually die?
>>>
>>> Humm... It should be "helpful" to think about infinity, where the
>>> program is being executed on a system that never dies. Its output is
>>> being observed by beings that never die.
>>>
>>> Does the program halt in the realm of the infinite?
>>
>> I don't know what this means.  I can answer about the mathematics, but I
>> don't know about these hypothetical computations that take time and are
>> "observed" by mythical creatures.
>>
>
> I was just wondering if the algorihtm might halt in a finite number of
> steps, but the number of steps would take a very long time. The Earth
> would be dead long before it gets a chance to halt. Does that make any
> sense at all? Humm...

Computation Theory is a theoretical discipline. We describe Turing
Machine operations in 'steps'. There is no concept of 'how fast' we
might be able to execture these steps, so for ANY finite number of
steps, we can compute a step rate to make that complete in an given
finite period of time.

Yes, we can conceive for machines that will take more steps then could
be possible executed by real physical hardware in the lifetime of the
universe, but if we can show that it will complete in a finite number of
steps, then we have shown that it is a 'Halting' computation, even if we
can never build a machine that can actually run it to completion.

Re: Black box halt decider is NOT a partial decider

<oBGKI.19827$o_5.3578@fx29.iad>

 copy mid

https://www.novabbs.com/devel/article-flat.php?id=18805&group=comp.theory#18805

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Subject: Re: Black box halt decider is NOT a partial decider
Newsgroups: comp.theory
References: <20210719214640.00000dfc@reddwarf.jmc>
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From: Rich...@Damon-Family.org (Richard Damon)
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 by: Richard Damon - Fri, 23 Jul 2021 21:34 UTC

On 7/23/21 2:20 PM, Chris M. Thomasson wrote:
> On 7/22/2021 2:52 PM, Richard Damon wrote:

>> The ACTUAL question for Computation Theory is does the Comutation reach
>> the Halt state in a FINITE number of steps.
>
> Theoretically, what if the program does halt in a FINITE number of steps
> but it would take so long that the Earth would be dead by then. How can
> the halt decider determine that?
>

The key is that Turing Machines are purely theoretical machines. They
run in 'steps' that don't have any actual fixed time period, so any
finite number of steps can be done in a finite time at some finite
computation rate.

It doesn't matter that we can't actually build hardware to do it that fast.

There are MANY things in Mathematics that we can never actually
physically compute exactly, but we talk about having an exact value.

Re: Black box halt decider is NOT a partial decider

<875yx0he2s.fsf@bsb.me.uk>

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https://www.novabbs.com/devel/article-flat.php?id=18808&group=comp.theory#18808

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From: ben.use...@bsb.me.uk (Ben Bacarisse)
Newsgroups: comp.theory
Subject: Re: Black box halt decider is NOT a partial decider
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 by: Ben Bacarisse - Fri, 23 Jul 2021 22:15 UTC

"Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> writes:

> On 7/22/2021 2:10 PM, Ben Bacarisse wrote:
>> "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> writes:
>>
>>> On 7/21/2021 5:17 AM, Ben Bacarisse wrote:
>>>> "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> writes:
>>>>
>>>>> For some stupid reason I always thought that the halting problem
>>>>> extends to all problems, and all programs.
>>>> It is a problem in mathematics and, like all mathematics, it is based on
>>>> sound definitions. It says nothing about "all programs" unless "all
>>>> programs" is a well-specified set. In that case, "all programs" might
>>>> well have a halting problem, and might even have a halting theorem.
>>>> The problem is always grounded to the context of some formal model of
>>>> computation like Turing machines, recursive functions or the lambda
>>>> calculus. I say "always" but that has to exclude comp.theory which is
>>>> dominated by silly ideas coming from people who don't know much about
>>>> such format models.
>>>>
>>>>> Well, here is some pure sarcasm:
>>>>>
>>>>> Every program halts because they will not get to run
>>>>> forever... Eventually, Earth will die.
>>>> This is not just sarcasm. It's a plain fact.
>>>>
>>>
>>> Well, based on this fact, can we say everything on Earth halts because
>>> the planet will eventually die?
>>>
>>> Humm... It should be "helpful" to think about infinity, where the
>>> program is being executed on a system that never dies. Its output is
>>> being observed by beings that never die.
>>>
>>> Does the program halt in the realm of the infinite?
>> I don't know what this means. I can answer about the mathematics, but I
>> don't know about these hypothetical computations that take time and are
>> "observed" by mythical creatures.
>
> I was just wondering if the algorihtm might halt in a finite number of
> steps, but the number of steps would take a very long time. The Earth
> would be dead long before it gets a chance to halt.

Would Sum[n=1..oo] 1/n^2 still be = (pi^2)/6 even if every addition took
a year?

> Does that make any sense at all? Humm...

--
Ben.

Re: Black box halt decider is NOT a partial decider

<sdffqm$jsh$1@gioia.aioe.org>

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https://www.novabbs.com/devel/article-flat.php?id=18811&group=comp.theory#18811

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From: chris.m....@gmail.com (Chris M. Thomasson)
Newsgroups: comp.theory
Subject: Re: Black box halt decider is NOT a partial decider
Date: Fri, 23 Jul 2021 15:28:35 -0700
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 by: Chris M. Thomasson - Fri, 23 Jul 2021 22:28 UTC

On 7/23/2021 3:15 PM, Ben Bacarisse wrote:
> "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> writes:
>
>> On 7/22/2021 2:10 PM, Ben Bacarisse wrote:
>>> "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> writes:
>>>
>>>> On 7/21/2021 5:17 AM, Ben Bacarisse wrote:
>>>>> "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> writes:
>>>>>
>>>>>> For some stupid reason I always thought that the halting problem
>>>>>> extends to all problems, and all programs.
>>>>> It is a problem in mathematics and, like all mathematics, it is based on
>>>>> sound definitions. It says nothing about "all programs" unless "all
>>>>> programs" is a well-specified set. In that case, "all programs" might
>>>>> well have a halting problem, and might even have a halting theorem.
>>>>> The problem is always grounded to the context of some formal model of
>>>>> computation like Turing machines, recursive functions or the lambda
>>>>> calculus. I say "always" but that has to exclude comp.theory which is
>>>>> dominated by silly ideas coming from people who don't know much about
>>>>> such format models.
>>>>>
>>>>>> Well, here is some pure sarcasm:
>>>>>>
>>>>>> Every program halts because they will not get to run
>>>>>> forever... Eventually, Earth will die.
>>>>> This is not just sarcasm. It's a plain fact.
>>>>>
>>>>
>>>> Well, based on this fact, can we say everything on Earth halts because
>>>> the planet will eventually die?
>>>>
>>>> Humm... It should be "helpful" to think about infinity, where the
>>>> program is being executed on a system that never dies. Its output is
>>>> being observed by beings that never die.
>>>>
>>>> Does the program halt in the realm of the infinite?
>>> I don't know what this means. I can answer about the mathematics, but I
>>> don't know about these hypothetical computations that take time and are
>>> "observed" by mythical creatures.
>>
>> I was just wondering if the algorihtm might halt in a finite number of
>> steps, but the number of steps would take a very long time. The Earth
>> would be dead long before it gets a chance to halt.
>
> Would Sum[n=1..oo] 1/n^2 still be = (pi^2)/6 even if every addition took
> a year?

Sure. It converges on that value. Gaining precision every step.

Sum[n=1..oo] 1/n^24 converges on 1.

>
>> Does that make any sense at all? Humm...
>

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