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devel / comp.theory / Re: Why do theory of computation problems require pure functions?

SubjectAuthor
* Why do theory of computation problems require pure functions?olcott
+- Why do theory of computation problems require pure functions?dklei...@gmail.com
+* Why do theory of computation problems require pure functions?André G. Isaak
|+* Why do theory of computation problems require pure functions?Jeff Barnett
||`* Why do theory of computation problems require pure functions?André G. Isaak
|| `- Why do theory of computation problems require pure functions?Jeff Barnett
|`* Why do theory of computation problems require pure functions?olcott
| +* Why do theory of computation problems require pure functions?Richard Damon
| |`* Why do theory of computation problems require pure functions?olcott
| | +* Why do theory of computation problems require pure functions?André G. Isaak
| | |+- Why do theory of computation problems require pure functions?olcott
| | |`* Why do theory of computation problems require pure functions?Richard Damon
| | | +* Why do theory of computation problems require pure functions?olcott
| | | |`* Why do theory of computation problems require pure functions?Richard Damon
| | | | `* Why do theory of computation problems require pure functions?olcott
| | | |  `* Why do theory of computation problems require pure functions?Richard Damon
| | | |   `- Why do theory of computation problems require pure functions?olcott
| | | `* Why do theory of computation problems require pure functions?André G. Isaak
| | |  `* Why do theory of computation problems require pure functions?Jeff Barnett
| | |   `* Why do theory of computation problems require pure functions?olcott
| | |    `* Why do theory of computation problems require pure functions?Richard Damon
| | |     `* Why do theory of computation problems require pure functions?olcott
| | |      `* Why do theory of computation problems require pure functions?Richard Damon
| | |       `* Why do theory of computation problems require pure functions?olcott
| | |        +* Why do theory of computation problems require pure functions?Ben Bacarisse
| | |        |`* Why do theory of computation problems require pure functions?olcott
| | |        | +- Why do theory of computation problems require pure functions?Richard Damon
| | |        | `- Why do theory of computation problems require pure functions?Ben Bacarisse
| | |        `- Why do theory of computation problems require pure functions?Richard Damon
| | `* Why do theory of computation problems require pure functions?Richard Damon
| |  `* Why do theory of computation problems require pure functions?olcott
| |   `* Why do theory of computation problems require pure functions?Richard Damon
| |    `* Why do theory of computation problems require pure functions?olcott
| |     `* Why do theory of computation problems require pure functions?Richard Damon
| |      `* Why do theory of computation problems require pure functions?olcott
| |       `* Why do theory of computation problems require pure functions?Richard Damon
| |        `* Why do theory of computation problems require pure functions?olcott
| |         `* Why do theory of computation problems require pure functions?Richard Damon
| |          `* Why do theory of computation problems require pure functions?Ben Bacarisse
| |           `* Why do theory of computation problems require pure functions?olcott
| |            +- Why do theory of computation problems require pure functions?Richard Damon
| |            `- Why do theory of computation problems require pure functions?Ben Bacarisse
| `* Why do theory of computation problems require pure functions?André G. Isaak
|  `* Why do theory of computation problems require pure functions?olcott
|   `* Why do theory of computation problems require pure functions?André G. Isaak
|    `- Why do theory of computation problems require pure functions?olcott
+- Why do theory of computation problems require pure functions?Richard Damon
`* Why do theory of computation problems require pure functions?Andy Walker
 +* Why do theory of computation problems require pure functions?olcott
 |+- Why do theory of computation problems require pure functions?Richard Damon
 |`* Why do theory of computation problems require pure functions?André G. Isaak
 | `* Why do theory of computation problems require pure functions?olcott
 |  +* Why do theory of computation problems require pure functions?Richard Damon
 |  |`* Why do theory of computation problems require pure functions?olcott
 |  | +* Why do theory of computation problems require pure functions?Richard Damon
 |  | |`* Why do theory of computation problems require pure functions?olcott
 |  | | `* Why do theory of computation problems require pure functions?Richard Damon
 |  | |  `* Why do theory of computation problems require pure functions?olcott
 |  | |   `* Why do theory of computation problems require pure functions?Richard Damon
 |  | |    `* Why do theory of computation problems require pure functions?olcott
 |  | |     `* Why do theory of computation problems require pure functions?Richard Damon
 |  | |      `* Why do theory of computation problems require pure functions?olcott
 |  | |       `* Why do theory of computation problems require pure functions?Richard Damon
 |  | |        `* Why do theory of computation problems require pure functions?olcott
 |  | |         `* Why do theory of computation problems require pure functions?Richard Damon
 |  | |          `* Why do theory of computation problems require pure functions?olcott
 |  | |           `* Why do theory of computation problems require pure functions?Richard Damon
 |  | |            `* Why do theory of computation problems require pure functions?olcott
 |  | |             `* Why do theory of computation problems require pure functions?Richard Damon
 |  | |              `* Why do theory of computation problems require pure functions?olcott
 |  | |               `- Why do theory of computation problems require pure functions?Richard Damon
 |  | `- Why do theory of computation problems require pure functions?Ben Bacarisse
 |  +* Why do theory of computation problems require pure functions?André G. Isaak
 |  |`* Why do theory of computation problems require pure functions?olcott
 |  | +* Why do theory of computation problems require pure functions?André G. Isaak
 |  | |`* Why do theory of computation problems require pure functions?olcott
 |  | | `* Why do theory of computation problems require pure functions?Richard Damon
 |  | |  `* Why do theory of computation problems require pure functions?olcott
 |  | |   +* Why do theory of computation problems require pure functions?Richard Damon
 |  | |   |`* Why do theory of computation problems require pure functions?olcott
 |  | |   | `* Why do theory of computation problems require pure functions?Richard Damon
 |  | |   |  `* Why do theory of computation problems require pure functions?olcott
 |  | |   |   +- Why do theory of computation problems require pure functions?Richard Damon
 |  | |   |   `* Why do theory of computation problems require pure functions?André G. Isaak
 |  | |   |    `* Why do theory of computation problems require pure functions?olcott
 |  | |   |     +* Why do theory of computation problems require pure functions?André G. Isaak
 |  | |   |     |`* Why do theory of computation problems require pure functions?olcott
 |  | |   |     | +* Why do theory of computation problems require pure functions?André G. Isaak
 |  | |   |     | |+- Why do theory of computation problems require pure functions?Richard Damon
 |  | |   |     | |+* Why do theory of computation problems require pure functions?olcott
 |  | |   |     | ||+* Why do theory of computation problems require pure functions?Richard Damon
 |  | |   |     | |||`* Why do theory of computation problems require pure functions?olcott
 |  | |   |     | ||| +* Why do theory of computation problems require pure functions?André G. Isaak
 |  | |   |     | ||| |`* Why do theory of computation problems require pure functions?André G. Isaak
 |  | |   |     | ||| | +* Why do theory of computation problems require pure functions?olcott
 |  | |   |     | ||| | |+* Why do theory of computation problems require pure functions?André G. Isaak
 |  | |   |     | ||| | ||`* Why do theory of computation problems require pure functions?[ decidability deciolcott
 |  | |   |     | ||| | || `- Why do theory of computation problems require pure functions?[André G. Isaak
 |  | |   |     | ||| | |`- Why do theory of computation problems require pure functions?Richard Damon
 |  | |   |     | ||| | `* Why do theory of computation problems require pure functions?olcott
 |  | |   |     | ||| |  `* Why do theory of computation problems require pure functions?André G. Isaak
 |  | |   |     | ||| `- Why do theory of computation problems require pure functions?Richard Damon
 |  | |   |     | ||`- Why do theory of computation problems require pure functions?André G. Isaak
 |  | |   |     | |`* Why do theory of computation problems require pure functions?Malcolm McLean
 |  | |   |     | `* Why do theory of computation problems require pure functions?Jeff Barnett
 |  | |   |     `- Why do theory of computation problems require pure functions?Richard Damon
 |  | |   `* Why do theory of computation problems require pure functions?Ben Bacarisse
 |  | `* Why do theory of computation problems require pure functions?Richard Damon
 |  `* Why do theory of computation problems require pure functions?Ben Bacarisse
 `* Why do theory of computation problems require pure functions?Ben Bacarisse

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Re: Why do theory of computation problems require pure functions? [defeating Rice]

<87o88o8bc2.fsf@bsb.me.uk>

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From: ben.use...@bsb.me.uk (Ben Bacarisse)
Newsgroups: comp.theory
Subject: Re: Why do theory of computation problems require pure functions? [defeating Rice]
Date: Sun, 19 Sep 2021 23:11:41 +0100
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 by: Ben Bacarisse - Sun, 19 Sep 2021 22:11 UTC

olcott <NoOne@NoWhere.com> writes:

> Ĥ.qx applied to ⟨Ĥ⟩ ⟨Ĥ⟩ has the pathological self-reference(Olcott 2004) error.
>
> H applied to ⟨Ĥ⟩ ⟨Ĥ⟩ does not have the pathological
> self-reference(Olcott 2004) error.

Silly terms aside, you tell us that, for your actual H,

H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ |- H.qy

or at least that is should do that. And then you tell us that, in fact,

Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ |- Ĥ.qn

But both can't be true since identical state transition graphs generate
identical machine configuration sequences when presented with identical
inputs. You have no answer to this other than to keep stating both
facts about your TM, one of which much be false.

--
Ben.

Re: Why do theory of computation problems require pure functions?

<87ilyw8amx.fsf@bsb.me.uk>

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From: ben.use...@bsb.me.uk (Ben Bacarisse)
Newsgroups: comp.theory
Subject: Re: Why do theory of computation problems require pure functions?
Date: Sun, 19 Sep 2021 23:26:46 +0100
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 by: Ben Bacarisse - Sun, 19 Sep 2021 22:26 UTC

olcott <NoOne@NoWhere.com> writes:

> On 9/18/2021 4:51 PM, Ben Bacarisse wrote:
>> olcott <NoOne@NoWhere.com> writes:
>>
>>> When H is defined as a simulating halt decider then H correctly
>>> decides the halt status of ⟨Ĥ⟩ ⟨Ĥ⟩.
>> Not according to you. You agree that H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ should transition to
>> H.qy
>
> I never said anything like that so I am stopping at your first fib.
> Furthermore I have repeated H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ transitions to H.qn many
> times.

Liar:

"No nitwit H ⟨Ĥ⟩ ⟨Ĥ⟩ transitions to H.qy as I have told you many times"
[Message-ID: <xo6dnWS9F6hkHKT8nZ2dnUU7-LfNnZ2d@giganews.com>]

"H applied to ⟨Ĥ⟩ ⟨Ĥ⟩ correctly transitions to H.qy"
[Message-ID: <caKdncaNf93r3dv8nZ2dnUU7-UfNnZ2d@giganews.com>]

and when I stated it:

|| If your H has any pretensions
|| of being a halt decider, it should accept that string:
||
|| H.q0 <H^><H^> |- H.qy

You agreed and claimed to have said so may times:

| I have already said that a bunch of times yet you did not notice
| because you diligently want to remain focused in disagreement mode.

Now you say you repeated many times that H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ transitions to
H.qn. Which is it? On which occasions were lies?

--
Ben.

Re: Why do theory of computation problems require pure functions?

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Subject: Re: Why do theory of computation problems require pure functions?
From: malcolm....@gmail.com (Malcolm McLean)
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 by: Malcolm McLean - Sun, 19 Sep 2021 22:36 UTC

On Sunday, 19 September 2021 at 22:38:41 UTC+1, Ben Bacarisse wrote:
> Malcolm McLean <malcolm.ar...@gmail.com> writes:
>
> > On Saturday, 18 September 2021 at 23:55:52 UTC+1, André G. Isaak wrote:
> >> On 2021-09-18 16:32, olcott wrote:
> >>
> >> >
> >> > I just defeated Rice's theorem, the other details are for another day.
> >> How exactly have you managed to do that?
> >>
> >> Unless you know which is correct, your H1/H pair are unable to reach a
> >> decision at all regarding halting.
> >>
> > We construct two halt deciders, which are known to be correct, other
> > than for "pathological" inputs. When fed such a "pathological" input,
> > one returns true and the other returns false.
> >
> > Therefore using the two halt deciders and selecting the instances where
> > they disagree, we have classified the "pathological inputs", something that
> > Rice's theorem states that cannot be achieved.
>
> Why do you say that? Surely that depends entirely on the parts you put
> in scare quotes. PO (deliberately?) flip-lops between stating that
> "pathological" inputs are characterised by a syntactic pattern and by a
> semantic property. Why do you even think he knows which one he is
> talking about today?
>
I'm just summarising PO's argument so that others can understand where he
is coming from.
You can poke holes in the argument, of course, but to try to do that at the same
time as summarising it would be unfiar and counter-productive.

Re: Why do theory of computation problems require pure functions? [ PSR error]

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Subject: Re: Why do theory of computation problems require pure functions? [
PSR error]
Newsgroups: comp.theory
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From: Rich...@Damon-Family.org (Richard Damon)
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 by: Richard Damon - Sun, 19 Sep 2021 22:59 UTC

On 9/19/21 3:31 PM, olcott wrote:
> On 9/19/2021 2:22 PM, Andy Walker wrote:
>> On 19/09/2021 19:33, olcott wrote:
>>> The halting theorem is based on an artificially contrived example
>>
>>      Not the /theorem/;  one particular proof [of several well-
>> known proofs] is based on that, others are not.
>>
>>> that would never actually occur in actual practice.
>>
>>      Depends what you mean by "actual practice";  it occurs
>> [subject to the caveat in my next paragraph] rather often in
>> discussions of the HP, and it occurs [ditto] in almost all C
>> programs [just as the sequence 31415926535 occurs in the decimal
>> expansion of almost all integers, though rarely in those with
>> relatively few digits].
>>
>>>                               In actual
>>> practice we would only actually need H.
>>
>>      You do realise that the program "H" doesn't actually
>> exist?  So it is at least as rare/artificial as "H^".
>>
>
> void P(u32 x)
> {
>
>   if (H(x, x))
>     HERE: goto HERE;
> }
>
> u32 PSR_Olcott_2004(u32 P)
> {
>   return H1(P,P) != H(P,P);
> }
>
> int main()
> {
>   Output("Pathological Self-Reference(Olcott 2004) = ",
>           PSR_Olcott_2004((u32) P));
> }
>
> You can't just drop into the middle of a conversation and expect to have
> the proper context.
>
> H does exist yet gets the wrong answer as detected by H1 that gets the
> right answer.
>

Linz H does not exist, read the proof. It begin by presuming it exists
and shows that that leads to a contradiction, so it can't exist.

PO-H is claimed to exist. It has been shown to be wrong, as it says that
for the H^ built on it, H^(H^) will be non-halting when it actually does
Halt, You seem to now claim that is ok, because H's twin H1 gets the
right answer, but H1 is not H, so it doesn't actually count here.

There is also the question if H is even qualified to be a halt decider,
as there is some question if it is a computation, always giving the same
answer for a given set of inputs in all cases. This comes down to a bit
of figuring out WHICH of severl

>>> The odd-man-out system does correctly decide an input that was
>>> artificially contrived to specifically have the pathological
>>> self-reference error (Olcott 2004) for either H or H1. All of the
>>> rest of the cases are simply correctly decided by either H or H1.
>>
>>      No they aren't;  by Rice's theorem if for no other
>> reason, assuming that you eventually manage to produce a
>> workable definition of "pathological self-reference".
>>
>
> I have it fully encoded as the function bodies of H and H1.
>

'Code' is not a definition of a property.

Note, The answer gotten from running the representation of a machine
into a decider is NOT a property of the machine, it might be the
decision of some property.

What is it that is the actual Semantic Property based on the behavior of
actually running P with various inputs is your decider correctly deciding?

It is TRIVIAL to write code that always gives the same answer as a piece
of code. That isn't what Rice's Theorem is about.

Re: Why do theory of computation problems require pure functions?

<877dfc891e.fsf@bsb.me.uk>

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From: ben.use...@bsb.me.uk (Ben Bacarisse)
Newsgroups: comp.theory
Subject: Re: Why do theory of computation problems require pure functions?
Date: Mon, 20 Sep 2021 00:01:17 +0100
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 by: Ben Bacarisse - Sun, 19 Sep 2021 23:01 UTC

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

> On Sunday, 19 September 2021 at 22:38:41 UTC+1, Ben Bacarisse wrote:
>> Malcolm McLean <malcolm.ar...@gmail.com> writes:
>>
>> > On Saturday, 18 September 2021 at 23:55:52 UTC+1, André G. Isaak wrote:
>> >> On 2021-09-18 16:32, olcott wrote:
>> >>
>> >> >
>> >> > I just defeated Rice's theorem, the other details are for another day.
>> >> How exactly have you managed to do that?
>> >>
>> >> Unless you know which is correct, your H1/H pair are unable to reach a
>> >> decision at all regarding halting.
>> >>
>> > We construct two halt deciders, which are known to be correct, other
>> > than for "pathological" inputs. When fed such a "pathological" input,
>> > one returns true and the other returns false.
>> >
>> > Therefore using the two halt deciders and selecting the instances where
>> > they disagree, we have classified the "pathological inputs", something that
>> > Rice's theorem states that cannot be achieved.
>>
>> Why do you say that? Surely that depends entirely on the parts you put
>> in scare quotes. PO (deliberately?) flip-lops between stating that
>> "pathological" inputs are characterised by a syntactic pattern and by a
>> semantic property. Why do you even think he knows which one he is
>> talking about today?
>>
> I'm just summarising PO's argument so that others can understand where
> he is coming from.

So help me understand where he is coming from today. Is he wrong
because two TMs that decide trivial properties don't refute Rice, or is
he wrong because even one would do the job just as well as two?

--
Ben.

Re: Why do theory of computation problems require pure functions?

<95d4a88f-8fbe-4151-a6bf-c83103d77f1bn@googlegroups.com>

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Subject: Re: Why do theory of computation problems require pure functions?
From: malcolm....@gmail.com (Malcolm McLean)
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 by: Malcolm McLean - Sun, 19 Sep 2021 23:23 UTC

On Monday, 20 September 2021 at 00:01:19 UTC+1, Ben Bacarisse wrote:
> Malcolm McLean <malcolm.ar...@gmail.com> writes:
>
> > On Sunday, 19 September 2021 at 22:38:41 UTC+1, Ben Bacarisse wrote:
> >> Malcolm McLean <malcolm.ar...@gmail.com> writes:
> >>
> >> > On Saturday, 18 September 2021 at 23:55:52 UTC+1, André G. Isaak wrote:
> >> >> On 2021-09-18 16:32, olcott wrote:
> >> >>
> >> >> >
> >> >> > I just defeated Rice's theorem, the other details are for another day.
> >> >> How exactly have you managed to do that?
> >> >>
> >> >> Unless you know which is correct, your H1/H pair are unable to reach a
> >> >> decision at all regarding halting.
> >> >>
> >> > We construct two halt deciders, which are known to be correct, other
> >> > than for "pathological" inputs. When fed such a "pathological" input,
> >> > one returns true and the other returns false.
> >> >
> >> > Therefore using the two halt deciders and selecting the instances where
> >> > they disagree, we have classified the "pathological inputs", something that
> >> > Rice's theorem states that cannot be achieved.
> >>
> >> Why do you say that? Surely that depends entirely on the parts you put
> >> in scare quotes. PO (deliberately?) flip-lops between stating that
> >> "pathological" inputs are characterised by a syntactic pattern and by a
> >> semantic property. Why do you even think he knows which one he is
> >> talking about today?
> >>
> > I'm just summarising PO's argument so that others can understand where
> > he is coming from.
> So help me understand where he is coming from today. Is he wrong
> because two TMs that decide trivial properties don't refute Rice, or is
> he wrong because even one would do the job just as well as two?
>
The snag I see is that the two machines cannot be built, unless we define
"pathological input" in a very narrow way, so narrow that it doesn't constitute
one of the properties Rice was talking about.

But there might be other weaknesses in the argument.

Re: Why do theory of computation problems require pure functions?

<87y27s6ssl.fsf@bsb.me.uk>

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https://www.novabbs.com/devel/article-flat.php?id=21460&group=comp.theory#21460

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From: ben.use...@bsb.me.uk (Ben Bacarisse)
Newsgroups: comp.theory
Subject: Re: Why do theory of computation problems require pure functions?
Date: Mon, 20 Sep 2021 00:37:30 +0100
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 by: Ben Bacarisse - Sun, 19 Sep 2021 23:37 UTC

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

> On Monday, 20 September 2021 at 00:01:19 UTC+1, Ben Bacarisse wrote:
>> Malcolm McLean <malcolm.ar...@gmail.com> writes:
>>
>> > On Sunday, 19 September 2021 at 22:38:41 UTC+1, Ben Bacarisse wrote:
>> >> Malcolm McLean <malcolm.ar...@gmail.com> writes:
>> >>
>> >> > On Saturday, 18 September 2021 at 23:55:52 UTC+1, André G. Isaak wrote:
>> >> >> On 2021-09-18 16:32, olcott wrote:
>> >> >>
>> >> >> >
>> >> >> > I just defeated Rice's theorem, the other details are for another day.
>> >> >> How exactly have you managed to do that?
>> >> >>
>> >> >> Unless you know which is correct, your H1/H pair are unable to reach a
>> >> >> decision at all regarding halting.
>> >> >>
>> >> > We construct two halt deciders, which are known to be correct, other
>> >> > than for "pathological" inputs. When fed such a "pathological" input,
>> >> > one returns true and the other returns false.
>> >> >
>> >> > Therefore using the two halt deciders and selecting the instances where
>> >> > they disagree, we have classified the "pathological inputs", something that
>> >> > Rice's theorem states that cannot be achieved.
>> >>
>> >> Why do you say that? Surely that depends entirely on the parts you put
>> >> in scare quotes. PO (deliberately?) flip-lops between stating that
>> >> "pathological" inputs are characterised by a syntactic pattern and by a
>> >> semantic property. Why do you even think he knows which one he is
>> >> talking about today?
>> >>
>> > I'm just summarising PO's argument so that others can understand where
>> > he is coming from.
>>
>> So help me understand where he is coming from today. Is he wrong
>> because two TMs that decide trivial properties don't refute Rice, or is
>> he wrong because even one would do the job just as well as two?
>>
> The snag I see is that the two machines cannot be built, unless we
> define "pathological input" in a very narrow way, so narrow that it
> doesn't constitute one of the properties Rice was talking about.

That does not help me understand where he is coming from. Is that what
he is doing today?

You are not summarising his argument, but flattering it by suggesting PO
means something (one thing) by it.

--
Ben.

Re: Why do theory of computation problems require pure functions? [defeating Rice]

<87sfy06shz.fsf@bsb.me.uk>

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https://www.novabbs.com/devel/article-flat.php?id=21461&group=comp.theory#21461

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From: ben.use...@bsb.me.uk (Ben Bacarisse)
Newsgroups: comp.theory
Subject: Re: Why do theory of computation problems require pure functions? [defeating Rice]
Date: Mon, 20 Sep 2021 00:43:52 +0100
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 by: Ben Bacarisse - Sun, 19 Sep 2021 23:43 UTC

olcott <NoOne@NoWhere.com> writes:

> On 9/18/2021 4:54 PM, Ben Bacarisse wrote:
>> olcott <NoOne@NoWhere.com> writes:
>>
>>> H applied to ⟨Ĥ⟩ ⟨Ĥ⟩ correctly transitions to H.qy.
>>
>> Yet you keep telling us that and "exact copy" of H transitions to the
>> rejecting state when presented with that input of the tape. Identical
>> state transition functions determine the exact same sequence of machine
>> configurations given identical tape contents.
>
> Ĥ.qx applied to ⟨Ĥ⟩ ⟨Ĥ⟩ has the pathological self-reference(Olcott
> 2004) error.

It can have any error in it you like to invent, but tell us what happens
and that can't be true as well as what you say above.

But things have moved on because you are now just lying about
something. As well as "H applied to ⟨Ĥ⟩ ⟨Ĥ⟩ correctly transitions to
H.qy" you are telling me that "I have repeated H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ transitions
to H.qn many times".

Putting aside how many times you've said each of these, which one is
true and which one is the lie?

--
Ben.

Re: Why do theory of computation problems require pure functions?

<GdSdnbHQ5unrfNr8nZ2dnUU7-UfNnZ2d@giganews.com>

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Subject: Re: Why do theory of computation problems require pure functions?
Newsgroups: comp.theory
References: <a7WdnftR4JAUzNj8nZ2dnUU7-d_NnZ2d@giganews.com> <si4khe$1nvt$1@gioia.aioe.org> <mJmdnfaWlv7Kbdj8nZ2dnUU7-YHNnZ2d@giganews.com> <si4v6h$u4l$3@dont-email.me> <Nc6dnYeBOsuRntv8nZ2dnUU7-QfNnZ2d@giganews.com> <si531f$q3f$2@dont-email.me> <CtmdnXIC2u_Di9v8nZ2dnUU7-R3NnZ2d@giganews.com> <si55gs$aa2$1@dont-email.me> <L5-dnUtHucSVgNv8nZ2dnUU7-X_NnZ2d@giganews.com> <12r1J.107151$lC6.16042@fx41.iad> <caKdncaNf93r3dv8nZ2dnUU7-UfNnZ2d@giganews.com> <axr1J.55095$jm6.40535@fx07.iad> <4dqdnW74K8nv1Nv8nZ2dnUU7-d2dnZ2d@giganews.com> <Sds1J.75975$z%4.33404@fx37.iad> <0LKdnQW0_vXAz9v8nZ2dnUU7-RHNnZ2d@giganews.com> <si5o18$ca0$1@dont-email.me> <b8qdnUQWUNeC-Nv8nZ2dnUU7-cvNnZ2d@giganews.com> <si5p69$qpa$1@dont-email.me> <i6WdnR3uOcyR9Nv8nZ2dnUU7-TGdnZ2d@giganews.com> <si5qpm$srv$1@dont-email.me> <b885b582-6153-4184-8dad-aed5dfc83cecn@googlegroups.com> <87bl4o9rfk.fsf@bsb.me.uk> <9f3d89f7-6040-4d9f-96e8-4fb18bf6985fn@googlegroups.com>
From: NoO...@NoWhere.com (olcott)
Date: Sun, 19 Sep 2021 20:18:43 -0500
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 by: olcott - Mon, 20 Sep 2021 01:18 UTC

On 9/19/2021 5:36 PM, Malcolm McLean wrote:
> On Sunday, 19 September 2021 at 22:38:41 UTC+1, Ben Bacarisse wrote:
>> Malcolm McLean <malcolm.ar...@gmail.com> writes:
>>
>>> On Saturday, 18 September 2021 at 23:55:52 UTC+1, André G. Isaak wrote:
>>>> On 2021-09-18 16:32, olcott wrote:
>>>>
>>>>>
>>>>> I just defeated Rice's theorem, the other details are for another day.
>>>> How exactly have you managed to do that?
>>>>
>>>> Unless you know which is correct, your H1/H pair are unable to reach a
>>>> decision at all regarding halting.
>>>>
>>> We construct two halt deciders, which are known to be correct, other
>>> than for "pathological" inputs. When fed such a "pathological" input,
>>> one returns true and the other returns false.
>>>
>>> Therefore using the two halt deciders and selecting the instances where
>>> they disagree, we have classified the "pathological inputs", something that
>>> Rice's theorem states that cannot be achieved.
>>
>> Why do you say that? Surely that depends entirely on the parts you put
>> in scare quotes. PO (deliberately?) flip-lops between stating that
>> "pathological" inputs are characterised by a syntactic pattern and by a
>> semantic property. Why do you even think he knows which one he is
>> talking about today?
>>
> I'm just summarising PO's argument so that others can understand where he
> is coming from.
> You can poke holes in the argument, of course, but to try to do that at the same
> time as summarising it would be unfiar and counter-productive.
>

Pathological self-reference (Olcott 2004) is generically the case where
the evaluation whether an expression of language has a semantic property
cannot be correctly made because this expression of language has
self-reference.

Concretely one case of this is objectively assessed by this function:

u32 PSR_Olcott_2004(u32 P)
{ return H1(P,P) != H(P,P);
}

--
Copyright 2021 Pete Olcott

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

Re: Why do theory of computation problems require pure functions?

<GdSdnbDQ5umIf9r8nZ2dnUU7-UednZ2d@giganews.com>

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Subject: Re: Why do theory of computation problems require pure functions?
Newsgroups: comp.theory
References: <a7WdnftR4JAUzNj8nZ2dnUU7-d_NnZ2d@giganews.com>
<si4v6h$u4l$3@dont-email.me> <Nc6dnYeBOsuRntv8nZ2dnUU7-QfNnZ2d@giganews.com>
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From: NoO...@NoWhere.com (olcott)
Date: Sun, 19 Sep 2021 20:21:24 -0500
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 by: olcott - Mon, 20 Sep 2021 01:21 UTC

On 9/19/2021 6:23 PM, Malcolm McLean wrote:
> On Monday, 20 September 2021 at 00:01:19 UTC+1, Ben Bacarisse wrote:
>> Malcolm McLean <malcolm.ar...@gmail.com> writes:
>>
>>> On Sunday, 19 September 2021 at 22:38:41 UTC+1, Ben Bacarisse wrote:
>>>> Malcolm McLean <malcolm.ar...@gmail.com> writes:
>>>>
>>>>> On Saturday, 18 September 2021 at 23:55:52 UTC+1, André G. Isaak wrote:
>>>>>> On 2021-09-18 16:32, olcott wrote:
>>>>>>
>>>>>>>
>>>>>>> I just defeated Rice's theorem, the other details are for another day.
>>>>>> How exactly have you managed to do that?
>>>>>>
>>>>>> Unless you know which is correct, your H1/H pair are unable to reach a
>>>>>> decision at all regarding halting.
>>>>>>
>>>>> We construct two halt deciders, which are known to be correct, other
>>>>> than for "pathological" inputs. When fed such a "pathological" input,
>>>>> one returns true and the other returns false.
>>>>>
>>>>> Therefore using the two halt deciders and selecting the instances where
>>>>> they disagree, we have classified the "pathological inputs", something that
>>>>> Rice's theorem states that cannot be achieved.
>>>>
>>>> Why do you say that? Surely that depends entirely on the parts you put
>>>> in scare quotes. PO (deliberately?) flip-lops between stating that
>>>> "pathological" inputs are characterised by a syntactic pattern and by a
>>>> semantic property. Why do you even think he knows which one he is
>>>> talking about today?
>>>>
>>> I'm just summarising PO's argument so that others can understand where
>>> he is coming from.
>> So help me understand where he is coming from today. Is he wrong
>> because two TMs that decide trivial properties don't refute Rice, or is
>> he wrong because even one would do the job just as well as two?
>>
> The snag I see is that the two machines cannot be built, unless we define
> "pathological input" in a very narrow way, so narrow that it doesn't constitute
> one of the properties Rice was talking about.
>
> But there might be other weaknesses in the argument.
>

The two machines are already fully operational.
H1 is merely a copy of H.

H has pathological self-reference and H1 does not because P calls H yet
never calls H1.

void P1(u32 x)
{ if (H(x, x))
HERE: goto HERE;
}

u32 PSR_Olcott_2004(u32 P)
{ return H1(P,P) != H(P,P);
}

--
Copyright 2021 Pete Olcott

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

Re: Why do theory of computation problems require pure functions?

<si8pa3$37b$1@dont-email.me>

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https://www.novabbs.com/devel/article-flat.php?id=21464&group=comp.theory#21464

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From: agis...@gm.invalid (André G. Isaak)
Newsgroups: comp.theory
Subject: Re: Why do theory of computation problems require pure functions?
Date: Sun, 19 Sep 2021 19:48:51 -0600
Organization: Christians and Atheists United Against Creeping Agnosticism
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 by: André G. Isaak - Mon, 20 Sep 2021 01:48 UTC

On 2021-09-19 19:18, olcott wrote:
> On 9/19/2021 5:36 PM, Malcolm McLean wrote:
>> On Sunday, 19 September 2021 at 22:38:41 UTC+1, Ben Bacarisse wrote:
>>> Malcolm McLean <malcolm.ar...@gmail.com> writes:
>>>
>>>> On Saturday, 18 September 2021 at 23:55:52 UTC+1, André G. Isaak wrote:
>>>>> On 2021-09-18 16:32, olcott wrote:
>>>>>
>>>>>>
>>>>>> I just defeated Rice's theorem, the other details are for another
>>>>>> day.
>>>>> How exactly have you managed to do that?
>>>>>
>>>>> Unless you know which is correct, your H1/H pair are unable to reach a
>>>>> decision at all regarding halting.
>>>>>
>>>> We construct two halt deciders, which are known to be correct, other
>>>> than for "pathological" inputs. When fed such a "pathological" input,
>>>> one returns true and the other returns false.
>>>>
>>>> Therefore using the two halt deciders and selecting the instances where
>>>> they disagree, we have classified the "pathological inputs",
>>>> something that
>>>> Rice's theorem states that cannot be achieved.
>>>
>>> Why do you say that? Surely that depends entirely on the parts you put
>>> in scare quotes. PO (deliberately?) flip-lops between stating that
>>> "pathological" inputs are characterised by a syntactic pattern and by a
>>> semantic property. Why do you even think he knows which one he is
>>> talking about today?
>>>
>> I'm just summarising PO's argument so that others can understand where he
>> is coming from.
>> You can poke holes in the argument, of course, but to try to do that
>> at the same
>> time as summarising it would be unfiar and counter-productive.
>>
>
> Pathological self-reference (Olcott 2004) is generically the case where
> the evaluation whether an expression of language has a semantic property
> cannot be correctly made because this expression of language has

Your programs are written in C. C has well-defined syntactic and
semantic rules. Neither your H nor your P violate any of those rules, so
in what sense is there an 'error'. Just asserting that there is one
doesn't make it so.

Yes, your H(P, P) produces the wrong answer, but that doesn't mean
there's any sort of 'error' with P.

André

André

Re: Why do theory of computation problems require pure functions?

<77OdndEx-cAoddr8nZ2dnUU7-QOdnZ2d@giganews.com>

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Subject: Re: Why do theory of computation problems require pure functions?
Newsgroups: comp.theory
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From: NoO...@NoWhere.com (olcott)
Date: Sun, 19 Sep 2021 20:49:40 -0500
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 by: olcott - Mon, 20 Sep 2021 01:49 UTC

On 9/19/2021 6:37 PM, Ben Bacarisse wrote:
> Malcolm McLean <malcolm.arthur.mclean@gmail.com> writes:
>
>> On Monday, 20 September 2021 at 00:01:19 UTC+1, Ben Bacarisse wrote:
>>> Malcolm McLean <malcolm.ar...@gmail.com> writes:
>>>
>>>> On Sunday, 19 September 2021 at 22:38:41 UTC+1, Ben Bacarisse wrote:
>>>>> Malcolm McLean <malcolm.ar...@gmail.com> writes:
>>>>>
>>>>>> On Saturday, 18 September 2021 at 23:55:52 UTC+1, André G. Isaak wrote:
>>>>>>> On 2021-09-18 16:32, olcott wrote:
>>>>>>>
>>>>>>>>
>>>>>>>> I just defeated Rice's theorem, the other details are for another day.
>>>>>>> How exactly have you managed to do that?
>>>>>>>
>>>>>>> Unless you know which is correct, your H1/H pair are unable to reach a
>>>>>>> decision at all regarding halting.
>>>>>>>
>>>>>> We construct two halt deciders, which are known to be correct, other
>>>>>> than for "pathological" inputs. When fed such a "pathological" input,
>>>>>> one returns true and the other returns false.
>>>>>>
>>>>>> Therefore using the two halt deciders and selecting the instances where
>>>>>> they disagree, we have classified the "pathological inputs", something that
>>>>>> Rice's theorem states that cannot be achieved.
>>>>>
>>>>> Why do you say that? Surely that depends entirely on the parts you put
>>>>> in scare quotes. PO (deliberately?) flip-lops between stating that
>>>>> "pathological" inputs are characterised by a syntactic pattern and by a
>>>>> semantic property. Why do you even think he knows which one he is
>>>>> talking about today?
>>>>>
>>>> I'm just summarising PO's argument so that others can understand where
>>>> he is coming from.
>>>
>>> So help me understand where he is coming from today. Is he wrong
>>> because two TMs that decide trivial properties don't refute Rice, or is
>>> he wrong because even one would do the job just as well as two?
>>>
>> The snag I see is that the two machines cannot be built, unless we
>> define "pathological input" in a very narrow way, so narrow that it
>> doesn't constitute one of the properties Rice was talking about.
>
> That does not help me understand where he is coming from. Is that what
> he is doing today?
>
> You are not summarising his argument, but flattering it by suggesting PO
> means something (one thing) by it.
>

He summed it up accurately.

--
Copyright 2021 Pete Olcott

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

Re: Why do theory of computation problems require pure functions? [defeating Rice]

<r42dnY5Rb4T5d9r8nZ2dnUU7-VfNnZ2d@giganews.com>

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Subject: Re: Why do theory of computation problems require pure functions?
[defeating Rice]
Newsgroups: comp.theory
References: <a7WdnftR4JAUzNj8nZ2dnUU7-d_NnZ2d@giganews.com>
<si4khe$1nvt$1@gioia.aioe.org>
<mJmdnfaWlv7Kbdj8nZ2dnUU7-YHNnZ2d@giganews.com> <si4v6h$u4l$3@dont-email.me>
<Nc6dnYeBOsuRntv8nZ2dnUU7-QfNnZ2d@giganews.com> <si531f$q3f$2@dont-email.me>
<CtmdnXIC2u_Di9v8nZ2dnUU7-R3NnZ2d@giganews.com> <si55gs$aa2$1@dont-email.me>
<L5-dnUtHucSVgNv8nZ2dnUU7-X_NnZ2d@giganews.com>
<12r1J.107151$lC6.16042@fx41.iad>
<caKdncaNf93r3dv8nZ2dnUU7-UfNnZ2d@giganews.com> <87a6k9blco.fsf@bsb.me.uk>
<h7ydndYbPtVt_Nv8nZ2dnUU7-IWdnZ2d@giganews.com> <87sfy06shz.fsf@bsb.me.uk>
From: NoO...@NoWhere.com (olcott)
Date: Sun, 19 Sep 2021 20:56:51 -0500
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 by: olcott - Mon, 20 Sep 2021 01:56 UTC

On 9/19/2021 6:43 PM, Ben Bacarisse wrote:
> olcott <NoOne@NoWhere.com> writes:
>
>> On 9/18/2021 4:54 PM, Ben Bacarisse wrote:
>>> olcott <NoOne@NoWhere.com> writes:
>>>
>>>> H applied to ⟨Ĥ⟩ ⟨Ĥ⟩ correctly transitions to H.qy.
>>>
>>> Yet you keep telling us that and "exact copy" of H transitions to the
>>> rejecting state when presented with that input of the tape. Identical
>>> state transition functions determine the exact same sequence of machine
>>> configurations given identical tape contents.
>>
>> Ĥ.qx applied to ⟨Ĥ⟩ ⟨Ĥ⟩ has the pathological self-reference(Olcott
>> 2004) error.
>
> It can have any error in it you like to invent, but tell us what happens
> and that can't be true as well as what you say above.
>
> But things have moved on because you are now just lying about
> something. As well as "H applied to ⟨Ĥ⟩ ⟨Ĥ⟩ correctly transitions to
> H.qy" you are telling me that "I have repeated H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ transitions
> to H.qn many times".
>
> Putting aside how many times you've said each of these, which one is
> true and which one is the lie?
>

Ĥ.qx applied to ⟨Ĥ⟩ ⟨Ĥ⟩ does correctly decide that its input never halts
unless it aborts the simulation of its input.

H applied to ⟨Ĥ⟩ ⟨Ĥ⟩ sees that Ĥ applied to ⟨Ĥ⟩ transitions to Ĥ.qn and
thus transitions to H.qy

void P(u32 x)
{ if (H(x, x))
HERE: goto HERE;
}

I could not understand this myself until I saw H1(P,P).

Previously I always said that H applied to ⟨Ĥ⟩ ⟨Ĥ⟩ was too
complicated to untangle when two different halt deciders
must coordinate with each other.

--
Copyright 2021 Pete Olcott

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

Re: Why do theory of computation problems require pure functions?

<v6idnae2nraxdtr8nZ2dnUU7-UPNnZ2d@giganews.com>

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Subject: Re: Why do theory of computation problems require pure functions?
Newsgroups: comp.theory
References: <a7WdnftR4JAUzNj8nZ2dnUU7-d_NnZ2d@giganews.com>
<mJmdnfaWlv7Kbdj8nZ2dnUU7-YHNnZ2d@giganews.com> <si4v6h$u4l$3@dont-email.me>
<Nc6dnYeBOsuRntv8nZ2dnUU7-QfNnZ2d@giganews.com> <si531f$q3f$2@dont-email.me>
<CtmdnXIC2u_Di9v8nZ2dnUU7-R3NnZ2d@giganews.com> <si55gs$aa2$1@dont-email.me>
<L5-dnUtHucSVgNv8nZ2dnUU7-X_NnZ2d@giganews.com>
<12r1J.107151$lC6.16042@fx41.iad>
<caKdncaNf93r3dv8nZ2dnUU7-UfNnZ2d@giganews.com>
<axr1J.55095$jm6.40535@fx07.iad>
<4dqdnW74K8nv1Nv8nZ2dnUU7-d2dnZ2d@giganews.com>
<Sds1J.75975$z%4.33404@fx37.iad>
<0LKdnQW0_vXAz9v8nZ2dnUU7-RHNnZ2d@giganews.com> <si5o18$ca0$1@dont-email.me>
<b8qdnUQWUNeC-Nv8nZ2dnUU7-cvNnZ2d@giganews.com> <si5p69$qpa$1@dont-email.me>
<i6WdnR3uOcyR9Nv8nZ2dnUU7-TGdnZ2d@giganews.com> <si5qpm$srv$1@dont-email.me>
<b885b582-6153-4184-8dad-aed5dfc83cecn@googlegroups.com>
<87bl4o9rfk.fsf@bsb.me.uk>
<9f3d89f7-6040-4d9f-96e8-4fb18bf6985fn@googlegroups.com>
<GdSdnbHQ5unrfNr8nZ2dnUU7-UfNnZ2d@giganews.com> <si8pa3$37b$1@dont-email.me>
From: NoO...@NoWhere.com (olcott)
Date: Sun, 19 Sep 2021 21:00:11 -0500
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 by: olcott - Mon, 20 Sep 2021 02:00 UTC

On 9/19/2021 8:48 PM, André G. Isaak wrote:
> On 2021-09-19 19:18, olcott wrote:
>> On 9/19/2021 5:36 PM, Malcolm McLean wrote:
>>> On Sunday, 19 September 2021 at 22:38:41 UTC+1, Ben Bacarisse wrote:
>>>> Malcolm McLean <malcolm.ar...@gmail.com> writes:
>>>>
>>>>> On Saturday, 18 September 2021 at 23:55:52 UTC+1, André G. Isaak
>>>>> wrote:
>>>>>> On 2021-09-18 16:32, olcott wrote:
>>>>>>
>>>>>>>
>>>>>>> I just defeated Rice's theorem, the other details are for another
>>>>>>> day.
>>>>>> How exactly have you managed to do that?
>>>>>>
>>>>>> Unless you know which is correct, your H1/H pair are unable to
>>>>>> reach a
>>>>>> decision at all regarding halting.
>>>>>>
>>>>> We construct two halt deciders, which are known to be correct, other
>>>>> than for "pathological" inputs. When fed such a "pathological" input,
>>>>> one returns true and the other returns false.
>>>>>
>>>>> Therefore using the two halt deciders and selecting the instances
>>>>> where
>>>>> they disagree, we have classified the "pathological inputs",
>>>>> something that
>>>>> Rice's theorem states that cannot be achieved.
>>>>
>>>> Why do you say that? Surely that depends entirely on the parts you put
>>>> in scare quotes. PO (deliberately?) flip-lops between stating that
>>>> "pathological" inputs are characterised by a syntactic pattern and by a
>>>> semantic property. Why do you even think he knows which one he is
>>>> talking about today?
>>>>
>>> I'm just summarising PO's argument so that others can understand
>>> where he
>>> is coming from.
>>> You can poke holes in the argument, of course, but to try to do that
>>> at the same
>>> time as summarising it would be unfiar and counter-productive.
>>>
>>
>> Pathological self-reference (Olcott 2004) is generically the case
>> where the evaluation whether an expression of language has a semantic
>> property cannot be correctly made because this expression of language has
>
> Your programs are written in C. C has well-defined syntactic and
> semantic rules. Neither your H nor your P violate any of those rules, so
> in what sense is there an 'error'. Just asserting that there is one
> doesn't make it so.
>
> Yes, your H(P, P) produces the wrong answer, but that doesn't mean
> there's any sort of 'error' with P.
>
> André
>
> André

This is a brand new semantic error that I first discovered in 2004 and
was only able to concretely formalize in the last two weeks as

void P(u32 x)
{ if (H(x, x))
HERE: goto HERE;
}

u32 PSR_Olcott_2004(u32 P)
{ return H1(P,P) != H(P,P);
}

--
Copyright 2021 Pete Olcott

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

Re: Why do theory of computation problems require pure functions?

<B4S1J.42729$3p3.29291@fx16.iad>

 copy mid

https://www.novabbs.com/devel/article-flat.php?id=21468&group=comp.theory#21468

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Subject: Re: Why do theory of computation problems require pure functions?
Newsgroups: comp.theory
References: <a7WdnftR4JAUzNj8nZ2dnUU7-d_NnZ2d@giganews.com>
<si4v6h$u4l$3@dont-email.me> <Nc6dnYeBOsuRntv8nZ2dnUU7-QfNnZ2d@giganews.com>
<si531f$q3f$2@dont-email.me> <CtmdnXIC2u_Di9v8nZ2dnUU7-R3NnZ2d@giganews.com>
<si55gs$aa2$1@dont-email.me> <L5-dnUtHucSVgNv8nZ2dnUU7-X_NnZ2d@giganews.com>
<12r1J.107151$lC6.16042@fx41.iad>
<caKdncaNf93r3dv8nZ2dnUU7-UfNnZ2d@giganews.com>
<axr1J.55095$jm6.40535@fx07.iad>
<4dqdnW74K8nv1Nv8nZ2dnUU7-d2dnZ2d@giganews.com>
<Sds1J.75975$z%4.33404@fx37.iad>
<0LKdnQW0_vXAz9v8nZ2dnUU7-RHNnZ2d@giganews.com> <si5o18$ca0$1@dont-email.me>
<b8qdnUQWUNeC-Nv8nZ2dnUU7-cvNnZ2d@giganews.com> <si5p69$qpa$1@dont-email.me>
<i6WdnR3uOcyR9Nv8nZ2dnUU7-TGdnZ2d@giganews.com> <si5qpm$srv$1@dont-email.me>
<b885b582-6153-4184-8dad-aed5dfc83cecn@googlegroups.com>
<87bl4o9rfk.fsf@bsb.me.uk>
<9f3d89f7-6040-4d9f-96e8-4fb18bf6985fn@googlegroups.com>
<GdSdnbHQ5unrfNr8nZ2dnUU7-UfNnZ2d@giganews.com> <si8pa3$37b$1@dont-email.me>
<v6idnae2nraxdtr8nZ2dnUU7-UPNnZ2d@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/78.14.0
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 by: Richard Damon - Mon, 20 Sep 2021 02:10 UTC

On 9/19/21 10:00 PM, olcott wrote:
> On 9/19/2021 8:48 PM, André G. Isaak wrote:
>> On 2021-09-19 19:18, olcott wrote:
>>> On 9/19/2021 5:36 PM, Malcolm McLean wrote:
>>>> On Sunday, 19 September 2021 at 22:38:41 UTC+1, Ben Bacarisse wrote:
>>>>> Malcolm McLean <malcolm.ar...@gmail.com> writes:
>>>>>
>>>>>> On Saturday, 18 September 2021 at 23:55:52 UTC+1, André G. Isaak
>>>>>> wrote:
>>>>>>> On 2021-09-18 16:32, olcott wrote:
>>>>>>>
>>>>>>>>
>>>>>>>> I just defeated Rice's theorem, the other details are for
>>>>>>>> another day.
>>>>>>> How exactly have you managed to do that?
>>>>>>>
>>>>>>> Unless you know which is correct, your H1/H pair are unable to
>>>>>>> reach a
>>>>>>> decision at all regarding halting.
>>>>>>>
>>>>>> We construct two halt deciders, which are known to be correct, other
>>>>>> than for "pathological" inputs. When fed such a "pathological" input,
>>>>>> one returns true and the other returns false.
>>>>>>
>>>>>> Therefore using the two halt deciders and selecting the instances
>>>>>> where
>>>>>> they disagree, we have classified the "pathological inputs",
>>>>>> something that
>>>>>> Rice's theorem states that cannot be achieved.
>>>>>
>>>>> Why do you say that? Surely that depends entirely on the parts you put
>>>>> in scare quotes. PO (deliberately?) flip-lops between stating that
>>>>> "pathological" inputs are characterised by a syntactic pattern and
>>>>> by a
>>>>> semantic property. Why do you even think he knows which one he is
>>>>> talking about today?
>>>>>
>>>> I'm just summarising PO's argument so that others can understand
>>>> where he
>>>> is coming from.
>>>> You can poke holes in the argument, of course, but to try to do that
>>>> at the same
>>>> time as summarising it would be unfiar and counter-productive.
>>>>
>>>
>>> Pathological self-reference (Olcott 2004) is generically the case
>>> where the evaluation whether an expression of language has a semantic
>>> property cannot be correctly made because this expression of language
>>> has
>>
>> Your programs are written in C. C has well-defined syntactic and
>> semantic rules. Neither your H nor your P violate any of those rules,
>> so in what sense is there an 'error'. Just asserting that there is one
>> doesn't make it so.
>>
>> Yes, your H(P, P) produces the wrong answer, but that doesn't mean
>> there's any sort of 'error' with P.
>>
>> André
>>
>> André
>
>
> This is a brand new semantic error that I first discovered in 2004 and
> was only able to concretely formalize in the last two weeks as
>
> void P(u32 x)
> {
>   if (H(x, x))
>     HERE: goto HERE;
> }
>
> u32 PSR_Olcott_2004(u32 P)
> {
>   return H1(P,P) != H(P,P);
> }
>
>

This is NOT a semantic error.

It is an error in your own understanding of what the problem being asked is.

FAIL.

Re: Why do theory of computation problems require pure functions?

<t9S1J.112246$Kv2.105439@fx47.iad>

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https://www.novabbs.com/devel/article-flat.php?id=21469&group=comp.theory#21469

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Subject: Re: Why do theory of computation problems require pure functions?
Newsgroups: comp.theory
References: <a7WdnftR4JAUzNj8nZ2dnUU7-d_NnZ2d@giganews.com> <si4khe$1nvt$1@gioia.aioe.org> <mJmdnfaWlv7Kbdj8nZ2dnUU7-YHNnZ2d@giganews.com> <si4v6h$u4l$3@dont-email.me> <Nc6dnYeBOsuRntv8nZ2dnUU7-QfNnZ2d@giganews.com> <si531f$q3f$2@dont-email.me> <CtmdnXIC2u_Di9v8nZ2dnUU7-R3NnZ2d@giganews.com> <si55gs$aa2$1@dont-email.me> <L5-dnUtHucSVgNv8nZ2dnUU7-X_NnZ2d@giganews.com> <12r1J.107151$lC6.16042@fx41.iad> <caKdncaNf93r3dv8nZ2dnUU7-UfNnZ2d@giganews.com> <axr1J.55095$jm6.40535@fx07.iad> <4dqdnW74K8nv1Nv8nZ2dnUU7-d2dnZ2d@giganews.com> <Sds1J.75975$z%4.33404@fx37.iad> <0LKdnQW0_vXAz9v8nZ2dnUU7-RHNnZ2d@giganews.com> <si5o18$ca0$1@dont-email.me> <b8qdnUQWUNeC-Nv8nZ2dnUU7-cvNnZ2d@giganews.com> <si5p69$qpa$1@dont-email.me> <i6WdnR3uOcyR9Nv8nZ2dnUU7-TGdnZ2d@giganews.com> <si5qpm$srv$1@dont-email.me> <b885b582-6153-4184-8dad-aed5dfc83cecn@googlegroups.com> <87bl4o9rfk.fsf@bsb.me.uk> <9f3d89f7-6040-4d9f-96e8-4fb18bf6985fn@googlegroups.com> <GdSdnbHQ5unrfNr8nZ2dnUU7-UfNnZ2d@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/78.14.0
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Date: Sun, 19 Sep 2021 22:15:52 -0400
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 by: Richard Damon - Mon, 20 Sep 2021 02:15 UTC

On 9/19/21 9:18 PM, olcott wrote:
> On 9/19/2021 5:36 PM, Malcolm McLean wrote:
>> On Sunday, 19 September 2021 at 22:38:41 UTC+1, Ben Bacarisse wrote:
>>> Malcolm McLean <malcolm.ar...@gmail.com> writes:
>>>
>>>> On Saturday, 18 September 2021 at 23:55:52 UTC+1, André G. Isaak wrote:
>>>>> On 2021-09-18 16:32, olcott wrote:
>>>>>
>>>>>>
>>>>>> I just defeated Rice's theorem, the other details are for another
>>>>>> day.
>>>>> How exactly have you managed to do that?
>>>>>
>>>>> Unless you know which is correct, your H1/H pair are unable to reach a
>>>>> decision at all regarding halting.
>>>>>
>>>> We construct two halt deciders, which are known to be correct, other
>>>> than for "pathological" inputs. When fed such a "pathological" input,
>>>> one returns true and the other returns false.
>>>>
>>>> Therefore using the two halt deciders and selecting the instances where
>>>> they disagree, we have classified the "pathological inputs",
>>>> something that
>>>> Rice's theorem states that cannot be achieved.
>>>
>>> Why do you say that? Surely that depends entirely on the parts you put
>>> in scare quotes. PO (deliberately?) flip-lops between stating that
>>> "pathological" inputs are characterised by a syntactic pattern and by a
>>> semantic property. Why do you even think he knows which one he is
>>> talking about today?
>>>
>> I'm just summarising PO's argument so that others can understand where he
>> is coming from.
>> You can poke holes in the argument, of course, but to try to do that
>> at the same
>> time as summarising it would be unfiar and counter-productive.
>>
>
> Pathological self-reference (Olcott 2004) is generically the case where
> the evaluation whether an expression of language has a semantic property
> cannot be correctly made because this expression of language has
> self-reference.
>
> Concretely one case of this is objectively assessed by this function:
>
> u32 PSR_Olcott_2004(u32 P)
> {
>   return H1(P,P) != H(P,P);
> }
>

So PSR_Olcott_2004 fails at its job because it gives different answer to:

u32 P1(u32 P) {
if(H1(P,P)) {
while(1) continue;
}
}

u32 P2(u32 P) {
if(H2(P,P)) {
while(1) continue;
}
}

Which either should both display the problem or nether, but PSR
categorizes them differently.

FAIL.

Re: Why do theory of computation problems require pure functions?

<si8r5f$npo$1@dont-email.me>

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From: agis...@gm.invalid (André G. Isaak)
Newsgroups: comp.theory
Subject: Re: Why do theory of computation problems require pure functions?
Date: Sun, 19 Sep 2021 20:20:29 -0600
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 by: André G. Isaak - Mon, 20 Sep 2021 02:20 UTC

On 2021-09-19 20:00, olcott wrote:

> This is a brand new semantic error that I first discovered in 2004 and
> was only able to concretely formalize in the last two weeks as
>
> void P(u32 x)
> {
>   if (H(x, x))
>     HERE: goto HERE;
> }
>
> u32 PSR_Olcott_2004(u32 P)
> {
>   return H1(P,P) != H(P,P);
> }

Those are simply lines of code. They don't 'formalize' anything. Finding
that two procedure calls don't give the same result doesn't signal any
sort of error.

The semantics of C are governed by the C standard. Unless you can point
to some specific aspect of C semantics that are being violated, you
can't call this a 'semantic error'.

André

--
To email remove 'invalid' & replace 'gm' with well known Google mail
service.

Re: Why do theory of computation problems require pure functions? [defeating Rice]

<lfS1J.112247$Kv2.31281@fx47.iad>

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https://www.novabbs.com/devel/article-flat.php?id=21471&group=comp.theory#21471

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Subject: Re: Why do theory of computation problems require pure functions?
[defeating Rice]
Newsgroups: comp.theory
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 by: Richard Damon - Mon, 20 Sep 2021 02:22 UTC

On 9/19/21 9:56 PM, olcott wrote:
> On 9/19/2021 6:43 PM, Ben Bacarisse wrote:
>> olcott <NoOne@NoWhere.com> writes:
>>
>>> On 9/18/2021 4:54 PM, Ben Bacarisse wrote:
>>>> olcott <NoOne@NoWhere.com> writes:
>>>>
>>>>> H applied to ⟨Ĥ⟩ ⟨Ĥ⟩ correctly transitions to H.qy.
>>>>
>>>> Yet you keep telling us that and "exact copy" of H transitions to the
>>>> rejecting state when presented with that input of the tape.  Identical
>>>> state transition functions determine the exact same sequence of machine
>>>> configurations given identical tape contents.
>>>
>>> Ĥ.qx applied to ⟨Ĥ⟩ ⟨Ĥ⟩ has the pathological self-reference(Olcott
>>> 2004) error.
>>
>> It can have any error in it you like to invent, but tell us what happens
>> and that can't be true as well as what you say above.
>>
>> But things have moved on because you are now just lying about
>> something.  As well as "H applied to ⟨Ĥ⟩ ⟨Ĥ⟩ correctly transitions to
>> H.qy" you are telling me that "I have repeated H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ transitions
>> to H.qn many times".
>>
>> Putting aside how many times you've said each of these, which one is
>> true and which one is the lie?
>>
>
> Ĥ.qx applied to ⟨Ĥ⟩ ⟨Ĥ⟩ does correctly decide that its input never halts
> unless it aborts the simulation of its input.

Except that isn't the queston. It is a fixed fact that the code at H^.qx
WILL abort the simulation, and that if that input was put to a UTM (or
other true simulator) it will Halt.

H^.qx is thsu wrong.

>
> H applied to ⟨Ĥ⟩ ⟨Ĥ⟩ sees that Ĥ applied to ⟨Ĥ⟩ transitions to Ĥ.qn and
> thus transitions to H.qy

But if my POOP decoder ring is working right, this 'H' isn't the same H
that P uses, but is the 'copy' of H, actually called H1, that isn't
computationally equivalent because it gives different answers.

SO, is H not a Computation, or is H1 not the same as H.

FAIL

>
> void P(u32 x)
> {
>   if (H(x, x))
>     HERE: goto HERE;
> }
>
> I could not understand this myself until I saw H1(P,P).
>
> Previously I always said that H applied to ⟨Ĥ⟩ ⟨Ĥ⟩ was too
> complicated to untangle when two different halt deciders
> must coordinate with each other.
>

Right DIFFERENT Halt deciders.

H1 getting it right does NOT prove anything, because H got it wrong.

You CAN'T equate both the code in H and in H1 to the same Turing Machine
H, as they don't give the same answers to the same input.

Thus your problem setup violates the problem statement.

You are NOT building the ^ template machine off the Halt Decider that
will try to correctly decide it.

FAIL.

Re: Why do theory of computation problems require pure functions?

<w_Wdnf4g-YWJZdr8nZ2dnUU7-Q3NnZ2d@giganews.com>

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Subject: Re: Why do theory of computation problems require pure functions?
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From: NoO...@NoWhere.com (olcott)
Date: Sun, 19 Sep 2021 21:55:15 -0500
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 by: olcott - Mon, 20 Sep 2021 02:55 UTC

On 9/19/2021 9:20 PM, André G. Isaak wrote:
> On 2021-09-19 20:00, olcott wrote:
>
>> This is a brand new semantic error that I first discovered in 2004 and
>> was only able to concretely formalize in the last two weeks as
>>
>> void P(u32 x)
>> {
>>    if (H(x, x))
>>      HERE: goto HERE;
>> }
>>
>> u32 PSR_Olcott_2004(u32 P)
>> {
>>    return H1(P,P) != H(P,P);
>> }
>
> Those are simply lines of code. They don't 'formalize' anything.

The rest of the fully opertational code that implements them does.

> Finding
> that two procedure calls don't give the same result doesn't signal any
> sort of error.
>

The Pathological self-reference error is why
"This sentence is not true" is neither true nor false.
It is (like H/P) self-contradictory.

> The semantics of C are governed by the C standard. Unless you can point
> to some specific aspect of C semantics that are being violated, you
> can't call this a 'semantic error'.
>
> André
>

--
Copyright 2021 Pete Olcott

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

Re: Why do theory of computation problems require pure functions?

<si91v5$gna$1@dont-email.me>

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https://www.novabbs.com/devel/article-flat.php?id=21474&group=comp.theory#21474

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From: agis...@gm.invalid (André G. Isaak)
Newsgroups: comp.theory
Subject: Re: Why do theory of computation problems require pure functions?
Date: Sun, 19 Sep 2021 22:16:36 -0600
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 by: André G. Isaak - Mon, 20 Sep 2021 04:16 UTC

On 2021-09-19 20:55, olcott wrote:
> On 9/19/2021 9:20 PM, André G. Isaak wrote:
>> On 2021-09-19 20:00, olcott wrote:
>>
>>> This is a brand new semantic error that I first discovered in 2004
>>> and was only able to concretely formalize in the last two weeks as
>>>
>>> void P(u32 x)
>>> {
>>>    if (H(x, x))
>>>      HERE: goto HERE;
>>> }
>>>
>>> u32 PSR_Olcott_2004(u32 P)
>>> {
>>>    return H1(P,P) != H(P,P);
>>> }
>>
>> Those are simply lines of code. They don't 'formalize' anything.
>
> The rest of the fully opertational code that implements them does.

Even if you have fully operational code, that still doesn't formalize
the notion of a 'pathological reference error'. For that you need an
actual DEFINITION. You've attempted a few but none of them have even
approached being a real formal definition. AFAICT 'pathological
reference error' is simply another way of saying 'something that Olcott
would like to sweep under the rug'.

>> Finding that two procedure calls don't give the same result doesn't
>> signal any sort of error.
>>
>
> The Pathological self-reference error is why
> "This sentence is not true" is neither true nor false.
> It is (like H/P) self-contradictory.

You've said this many times. It's simply not compelling. There's no
resemblance between the halting problem and the liar. While the liar
arguably has no truth value, P(P) has a perfectly well-defined halting
status which can easily be determined. It simply cannot be determined by
H. There's no 'error' involved; simply a limitation of what H (or any
other alleged halt decider) can actually do.

There's nothing 'erroneous' about P. You seem to claim that the error
arises only when it appears as an input to H (and even then, only when
the input to P is a description of P). The only way that that can be
sensibly interpreted is to view this as a claim that this isn't a valid
input to H because it falls outside the domain of the function H. But
since P(P) *is* a computation, that is simply an acknowledgement that H
is not a *universal* halt decider. By definition, a universal halt
decider must accept *any* valid computation as an input and must return
a result.

André

--
To email remove 'invalid' & replace 'gm' with well known Google mail
service.

Re: Why do theory of computation problems require pure functions?

<87ee9j7ess.fsf@bsb.me.uk>

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https://www.novabbs.com/devel/article-flat.php?id=21475&group=comp.theory#21475

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From: ben.use...@bsb.me.uk (Ben Bacarisse)
Newsgroups: comp.theory
Subject: Re: Why do theory of computation problems require pure functions?
Date: Mon, 20 Sep 2021 10:54:27 +0100
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 by: Ben Bacarisse - Mon, 20 Sep 2021 09:54 UTC

olcott <NoOne@NoWhere.com> writes:

> On 9/19/2021 6:37 PM, Ben Bacarisse wrote:
>> Malcolm McLean <malcolm.arthur.mclean@gmail.com> writes:
>>
>>> On Monday, 20 September 2021 at 00:01:19 UTC+1, Ben Bacarisse wrote:
>>>> Malcolm McLean <malcolm.ar...@gmail.com> writes:
>>>>
>>>>> On Sunday, 19 September 2021 at 22:38:41 UTC+1, Ben Bacarisse wrote:
>>>>>> Malcolm McLean <malcolm.ar...@gmail.com> writes:
>>>>>>
>>>>>>> On Saturday, 18 September 2021 at 23:55:52 UTC+1, André G. Isaak wrote:
>>>>>>>> On 2021-09-18 16:32, olcott wrote:
>>>>>>>>
>>>>>>>>>
>>>>>>>>> I just defeated Rice's theorem, the other details are for another day.
>>>>>>>> How exactly have you managed to do that?
>>>>>>>>
>>>>>>>> Unless you know which is correct, your H1/H pair are unable to reach a
>>>>>>>> decision at all regarding halting.
>>>>>>>>
>>>>>>> We construct two halt deciders, which are known to be correct, other
>>>>>>> than for "pathological" inputs. When fed such a "pathological" input,
>>>>>>> one returns true and the other returns false.
>>>>>>>
>>>>>>> Therefore using the two halt deciders and selecting the instances where
>>>>>>> they disagree, we have classified the "pathological inputs", something that
>>>>>>> Rice's theorem states that cannot be achieved.
>>>>>>
>>>>>> Why do you say that? Surely that depends entirely on the parts you put
>>>>>> in scare quotes. PO (deliberately?) flip-lops between stating that
>>>>>> "pathological" inputs are characterised by a syntactic pattern and by a
>>>>>> semantic property. Why do you even think he knows which one he is
>>>>>> talking about today?
>>>>>>
>>>>> I'm just summarising PO's argument so that others can understand where
>>>>> he is coming from.
>>>>
>>>> So help me understand where he is coming from today. Is he wrong
>>>> because two TMs that decide trivial properties don't refute Rice, or is
>>>> he wrong because even one would do the job just as well as two?
>>>>
>>> The snag I see is that the two machines cannot be built, unless we
>>> define "pathological input" in a very narrow way, so narrow that it
>>> doesn't constitute one of the properties Rice was talking about.
>> That does not help me understand where he is coming from. Is that what
>> he is doing today?
>>
>> You are not summarising his argument, but flattering it by suggesting PO
>> means something (one thing) by it.
>
> He summed it up accurately.

.... by leaving out the important bit. I note you too will not commit to
saying which mistake you are making today but that is likely just
because you have no idea what I'm saying. Let me try again: are you
wrong because the property is trivial (in the technical sense) or wrong
because it is not trivial and either of the two functions would
contravene the halting theorem (what you incorrectly describe as
"refuting") and therefore also Rice's theorem? I.e. is your recent plan
trivial or pointless?

At this point you should inject that quote of mine you are so enamoured
with. Maybe you'll get what it means this time. I can't remember the
details but it's something like "any algorithm that decides non-halting
in already a halt decider".

Mind you, since you've now moved on to deliberate, direct, lying to
confuse the bigger picture (i.e. what the halting problem is actually
about) I'm not sure these details are worth discussing anymore.

Which of

"No nitwit H ⟨Ĥ⟩ ⟨Ĥ⟩ transitions to H.qy as I have told you many times."

"I have repeated H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ transitions to H.qn many times."

Is true and which is, or was, a lie?

--
Ben.

Re: Why do theory of computation problems require pure functions? [defeating Rice]

<87bl4n7erw.fsf@bsb.me.uk>

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From: ben.use...@bsb.me.uk (Ben Bacarisse)
Newsgroups: comp.theory
Subject: Re: Why do theory of computation problems require pure functions? [defeating Rice]
Date: Mon, 20 Sep 2021 10:54:59 +0100
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 by: Ben Bacarisse - Mon, 20 Sep 2021 09:54 UTC

olcott <NoOne@NoWhere.com> writes:

> On 9/19/2021 6:43 PM, Ben Bacarisse wrote:

>> But things have moved on because you are now just lying about
>> something. As well as "H applied to ⟨Ĥ⟩ ⟨Ĥ⟩ correctly transitions to
>> H.qy" you are telling me that "I have repeated H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ transitions
>> to H.qn many times".
>> Putting aside how many times you've said each of these, which one is
>> true and which one is the lie?
>
> Ĥ.qx applied to ⟨Ĥ⟩ ⟨Ĥ⟩ does correctly decide that its input never
> halts unless it aborts the simulation of its input.

Won't answer? I am not surprised. Here are the two things you've been
very insistent upon (to the point of childish rudeness):

"No nitwit H ⟨Ĥ⟩ ⟨Ĥ⟩ transitions to H.qy as I have told you many times."

"I have repeated H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ transitions to H.qn many times."

Which is, or was, true and which is, or was, a lie?

--
Ben.

Re: Why do theory of computation problems require pure functions?

<875yuv7ei8.fsf@bsb.me.uk>

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From: ben.use...@bsb.me.uk (Ben Bacarisse)
Newsgroups: comp.theory
Subject: Re: Why do theory of computation problems require pure functions?
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 by: Ben Bacarisse - Mon, 20 Sep 2021 10:00 UTC

olcott <NoOne@NoWhere.com> writes:

> The two machines are already fully operational.
> H1 is merely a copy of H.

It's deceptive to call your secret C functions "machines". It hints at
the formality a clarity of Turing machines, but a TM that is a copy of
another will have exactly the same transfer function (i.e. it will never
compute a different result).

--
Ben.

Re: Why do theory of computation problems require pure functions?

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Subject: Re: Why do theory of computation problems require pure functions?
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From: Rich...@Damon-Family.org (Richard Damon)
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 by: Richard Damon - Mon, 20 Sep 2021 10:47 UTC

On 9/19/21 10:55 PM, olcott wrote:
> On 9/19/2021 9:20 PM, André G. Isaak wrote:
>> On 2021-09-19 20:00, olcott wrote:
>>
>>> This is a brand new semantic error that I first discovered in 2004
>>> and was only able to concretely formalize in the last two weeks as
>>>
>>> void P(u32 x)
>>> {
>>>    if (H(x, x))
>>>      HERE: goto HERE;
>>> }
>>>
>>> u32 PSR_Olcott_2004(u32 P)
>>> {
>>>    return H1(P,P) != H(P,P);
>>> }
>>
>> Those are simply lines of code. They don't 'formalize' anything.
>
> The rest of the fully opertational code that implements them does.
>
>> Finding that two procedure calls don't give the same result doesn't
>> signal any sort of error.
>>
>
> The Pathological self-reference error is why
> "This sentence is not true" is neither true nor false.
> It is (like H/P) self-contradictory.
>

That is meaningless in this context.

In what sense are you claiming that P doesn't have a truth value?

It is clear, and you have accepted, that P(P) does Halt when run as a
Computation. This is the proper value of the Question of does P(P) Halt.

In what way does that running not have a value?

The ONLY question you have shown to not have a value is the question,
"What Should H return when given the input <P> <P> to be right?"

That is NOT a question in view at this time, as once you have defined
this PSC_Olcott_2004 as a machine, you HAD to have made whatever wrong
choice to that question you are going to make.

If you issue that H is actually DEFINED as returning the rtght value,
then H is not a Computation, becuase it is not based on an actual
algorithm, and it also means that you haven't written code that
implements H because you can't write C code that actually implements
that either.

It seems what you have written is some code to implement the results of
faulty logic that you just assume/'stipulate' must be correct, but which
is actually unsound and wrong.

>> The semantics of C are governed by the C standard. Unless you can
>> point to some specific aspect of C semantics that are being violated,
>> you can't call this a 'semantic error'.
>>
>> André
>>
>
>

Re: Why do theory of computation problems require pure functions?

<xPudnZ8XN8DrDtX8nZ2dnUU7-THNnZ2d@giganews.com>

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Subject: Re: Why do theory of computation problems require pure functions?
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From: NoO...@NoWhere.com (olcott)
Date: Mon, 20 Sep 2021 08:58:13 -0500
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 by: olcott - Mon, 20 Sep 2021 13:58 UTC

On 9/20/2021 4:54 AM, Ben Bacarisse wrote:
> olcott <NoOne@NoWhere.com> writes:
>
>> On 9/19/2021 6:37 PM, Ben Bacarisse wrote:
>>> Malcolm McLean <malcolm.arthur.mclean@gmail.com> writes:
>>>
>>>> On Monday, 20 September 2021 at 00:01:19 UTC+1, Ben Bacarisse wrote:
>>>>> Malcolm McLean <malcolm.ar...@gmail.com> writes:
>>>>>
>>>>>> On Sunday, 19 September 2021 at 22:38:41 UTC+1, Ben Bacarisse wrote:
>>>>>>> Malcolm McLean <malcolm.ar...@gmail.com> writes:
>>>>>>>
>>>>>>>> On Saturday, 18 September 2021 at 23:55:52 UTC+1, André G. Isaak wrote:
>>>>>>>>> On 2021-09-18 16:32, olcott wrote:
>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> I just defeated Rice's theorem, the other details are for another day.
>>>>>>>>> How exactly have you managed to do that?
>>>>>>>>>
>>>>>>>>> Unless you know which is correct, your H1/H pair are unable to reach a
>>>>>>>>> decision at all regarding halting.
>>>>>>>>>
>>>>>>>> We construct two halt deciders, which are known to be correct, other
>>>>>>>> than for "pathological" inputs. When fed such a "pathological" input,
>>>>>>>> one returns true and the other returns false.
>>>>>>>>
>>>>>>>> Therefore using the two halt deciders and selecting the instances where
>>>>>>>> they disagree, we have classified the "pathological inputs", something that
>>>>>>>> Rice's theorem states that cannot be achieved.
>>>>>>>
>>>>>>> Why do you say that? Surely that depends entirely on the parts you put
>>>>>>> in scare quotes. PO (deliberately?) flip-lops between stating that
>>>>>>> "pathological" inputs are characterised by a syntactic pattern and by a
>>>>>>> semantic property. Why do you even think he knows which one he is
>>>>>>> talking about today?
>>>>>>>
>>>>>> I'm just summarising PO's argument so that others can understand where
>>>>>> he is coming from.
>>>>>
>>>>> So help me understand where he is coming from today. Is he wrong
>>>>> because two TMs that decide trivial properties don't refute Rice, or is
>>>>> he wrong because even one would do the job just as well as two?
>>>>>
>>>> The snag I see is that the two machines cannot be built, unless we
>>>> define "pathological input" in a very narrow way, so narrow that it
>>>> doesn't constitute one of the properties Rice was talking about.
>>> That does not help me understand where he is coming from. Is that what
>>> he is doing today?
>>>
>>> You are not summarising his argument, but flattering it by suggesting PO
>>> means something (one thing) by it.
>>
>> He summed it up accurately.
>
> ... by leaving out the important bit. I note you too will not commit to
> saying which mistake you are making today but that is likely just
> because you have no idea what I'm saying. Let me try again: are you
> wrong because the property is trivial (in the technical sense) or wrong
> because it is not trivial and either of the two functions would
> contravene the halting theorem (what you incorrectly describe as
> "refuting") and therefore also Rice's theorem? I.e. is your recent plan
> trivial or pointless?
>

"This sentence is not true" cannot be correctly evaluated as true or
false because it contradicts itself.

"This sentence is not true: 2 + 3 = 7" is true and does not congtradict
itself.

The same thing goes for
Olcott H1/H on input (P,P)
and Linz H/Ĥ.qx on input ⟨Ĥ⟩ ⟨Ĥ⟩

> At this point you should inject that quote of mine you are so enamoured
> with. Maybe you'll get what it means this time. I can't remember the
> details but it's something like "any algorithm that decides non-halting
> in already a halt decider".
>
> Mind you, since you've now moved on to deliberate, direct, lying to
> confuse the bigger picture (i.e. what the halting problem is actually
> about) I'm not sure these details are worth discussing anymore.
>
> Which of
>
> "No nitwit H ⟨Ĥ⟩ ⟨Ĥ⟩ transitions to H.qy as I have told you many times."
>
> "I have repeated H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ transitions to H.qn many times."
>
> Is true and which is, or was, a lie?
>

--
Copyright 2021 Pete Olcott

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

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