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computers / comp.ai.philosophy / Re: Why do theory of computation problems require pure functions? [ PSR error]

SubjectAuthor
* Why do theory of computation problems require pure functions?olcott
+* Re: Why do theory of computation problems require pure functions?olcott
|`- Re: Why do theory of computation problems require pure functions?olcott
`* Re: Why do theory of computation problems require pure functions?olcott
 +* Re: Why do theory of computation problems require pure functions?olcott
 |+- Re: Why do theory of computation problems require pure functions?[ decidability olcott
 |`* Re: Why do theory of computation problems require pure functions? [olcott
 | `* Re: Why do theory of computation problems require pure functions? [olcott
 |  +- Re: Why do theory of computation problems require pure functions? [Jeff Barnett
 |  `* Re: Why do theory of computation problems require pure functions? [olcott
 |   `- Re: Why do theory of computation problems require pure functions? [ PSR error]olcott
 +* Re: Why do theory of computation problems require pure functions?olcott
 |`- Re: Why do theory of computation problems require pure functions?olcott
 `- Re: Why do theory of computation problems require pure functions? [olcott

1
Why do theory of computation problems require pure functions?

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 by: olcott - Sat, 18 Sep 2021 02:40 UTC

Why do theory of computation problems require pure functions?

I am trying to write C code that would be acceptable to computer
scientists in the field of the theory of computation.

In computer programming, a pure function is a function that has the
following properties:

(1) The function return values are identical for identical arguments (no
variation with local static variables, non-local variables, mutable
reference arguments or input streams).

(2) The function application has no side effects (no mutation of local
static variables, non-local variables, mutable reference arguments or
input/output streams).

https://en.wikipedia.org/wiki/Pure_function#Compiler_optimizations

--
Copyright 2021 Pete Olcott

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

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 by: olcott - Sat, 18 Sep 2021 13:54 UTC

On 9/17/2021 11:50 PM, André G. Isaak wrote:
> On 2021-09-17 20:40, olcott wrote:
>> Why do theory of computation problems require pure functions?
>
> Because the theory of computation isn't about C or x86. It isn't about
> computer programs at all, nor about modern computers. Just because
> 'computation' and 'computer' share the same root doesn't mean they deal
> with the same set of phenomena. Remember that the theory of computation
> developed before there even were digital computers or programming
> languages.
>
> Computational theory is concerned with describing *mathematical*
> functions, and all mathematical functions are pure functions. A
> computation is a method for determining the value of the mathematical
> function f(x) for a given x. A computable function is one for which it
> is possible to construct a TM which, given an input string representing
> x, will determine the value of f(x).
>
> You can write computer programs which perform computations, but the
> majority of computer programs don't.
>
> If you really want to learn about the theory of computation, I'd suggest
> that you forget about C or x86 assembly or any sort of computer language
> altogether and focus on Turing Machines.
>
> And don't try to mentally translate anything you read about Turing
> Machines into computer languages. Don't think about loop counters, or
> calls, or machine addresses, because all of these things pertain to
> computers and computer programming rather than computations and they
> will get in the way of you actually understanding either turing machines
> or the theory of computation more generally.
>
> André
>

I only need to know this for one reason.

When my halt decider is examining the behavior of its input and the
input calls this halt decider in infinite recursion it cannot keep track
of the behavior of this input without having a single pseudo static
variable that is directly embedded in its machine code.

This pseudo static variable stores the ongoing execution trace. When the
variable is an ordinary local variable it loses all of its data between
each recursive simulation.

It still seems to be a pure function of its input in that
(1) The function return values are identical for identical arguments

--
Copyright 2021 Pete Olcott

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

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From: NoO...@NoWhere.com (olcott)
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 by: olcott - Sat, 18 Sep 2021 16:08 UTC

On 9/18/2021 10:44 AM, Richard Damon wrote:
> On 9/18/21 11:37 AM, olcott wrote:
>> On 9/18/2021 10:25 AM, Richard Damon wrote:
>>> On 9/18/21 11:19 AM, olcott wrote:
>>>> On 9/18/2021 10:13 AM, Richard Damon wrote:
>>>>> On 9/18/21 10:49 AM, olcott wrote:
>>>>>> On 9/18/2021 9:43 AM, Richard Damon wrote:
>>>>>>>
>>>>>>> On 9/18/21 9:54 AM, olcott wrote:
>>>>>>>> On 9/17/2021 11:50 PM, André G. Isaak wrote:
>>>>>>>>> On 2021-09-17 20:40, olcott wrote:
>>>>>>>>>> Why do theory of computation problems require pure functions?
>>>>>>>>>
>>>>>>>>> Because the theory of computation isn't about C or x86. It isn't
>>>>>>>>> about
>>>>>>>>> computer programs at all, nor about modern computers. Just because
>>>>>>>>> 'computation' and 'computer' share the same root doesn't mean they
>>>>>>>>> deal with the same set of phenomena. Remember that the theory of
>>>>>>>>> computation developed before there even were digital computers or
>>>>>>>>> programming languages.
>>>>>>>>>
>>>>>>>>> Computational theory is concerned with describing *mathematical*
>>>>>>>>> functions, and all mathematical functions are pure functions. A
>>>>>>>>> computation is a method for determining the value of the
>>>>>>>>> mathematical
>>>>>>>>> function f(x) for a given x. A computable function is one for
>>>>>>>>> which it
>>>>>>>>> is possible to construct a TM which, given an input string
>>>>>>>>> representing x, will determine the value of f(x).
>>>>>>>>>
>>>>>>>>> You can write computer programs which perform computations, but the
>>>>>>>>> majority of computer programs don't.
>>>>>>>>>
>>>>>>>>> If you really want to learn about the theory of computation, I'd
>>>>>>>>> suggest that you forget about C or x86 assembly or any sort of
>>>>>>>>> computer language altogether and focus on Turing Machines.
>>>>>>>>>
>>>>>>>>> And don't try to mentally translate anything you read about Turing
>>>>>>>>> Machines into computer languages. Don't think about loop
>>>>>>>>> counters, or
>>>>>>>>> calls, or machine addresses, because all of these things pertain to
>>>>>>>>> computers and computer programming rather than computations and
>>>>>>>>> they
>>>>>>>>> will get in the way of you actually understanding either turing
>>>>>>>>> machines or the theory of computation more generally.
>>>>>>>>>
>>>>>>>>> André
>>>>>>>>>
>>>>>>>>
>>>>>>>> I only need to know this for one reason.
>>>>>>>>
>>>>>>>> When my halt decider is examining the behavior of its input and the
>>>>>>>> input calls this halt decider in infinite recursion it cannot keep
>>>>>>>> track
>>>>>>>> of the behavior of this input without having a single pseudo static
>>>>>>>> variable that is directly embedded in its machine code.
>>>>>>>>
>>>>>>>> This pseudo static variable stores the ongoing execution trace.
>>>>>>>> When the
>>>>>>>> variable is an ordinary local variable it loses all of its data
>>>>>>>> between
>>>>>>>> each recursive simulation.
>>>>>>>>
>>>>>>>> It still seems to be a pure function of its input in that
>>>>>>>> (1) The function return values are identical for identical arguments
>>>>>>>>
>>>>>>>
>>>>>>> I think the key issue is that if you want to talk about the plain
>>>>>>> behavior of C / x86 code, then you need to talk about the ACTUAL
>>>>>>> behavior of that code, which means that the call to H within the
>>>>>>> simulated machine needs to be seen as a call to H, and NOT some
>>>>>>> logical
>>>>>>> transformation.
>>>>>>>
>>>>>>> If you want to do the transformation, your need to actually PROVE
>>>>>>> that
>>>>>>> this transform is legitimate under the conditions you want to make
>>>>>>> it,
>>>>>>> and that needs a very FORMAL argument based on accepted truths and
>>>>>>> principles. Your 'argument' based on H not affecting P until after it
>>>>>>> makes its decision so it can ignore its effect, is one of those
>>>>>>> arguments that just seems 'obvious' but you haven't actually
>>>>>>> proved it.
>>>>>>> You don't seem to uhderstand that nature of how to prove something
>>>>>>> like
>>>>>>> this.
>>>>>>>
>>>>>>> 'Obvious' things can be wrong, like it seems obvious that the
>>>>>>> order you
>>>>>>> add up a series shouldn't affect the result, even if the number of
>>>>>>> terms
>>>>>>> in infinite, but there are simple proofs to show that for SOME
>>>>>>> infinite
>>>>>>> sums, the order you take the terms can make a difference, dispite it
>>>>>>> seeming contrary to the nature of addition (infinities break a lot of
>>>>>>> common sense).
>>>>>>>
>>>>>>>
>>>>>>> A key point about your 'static' variable problem.
>>>>>>
>>>>>> There is only a single question here, not the myriad of questions that
>>>>>> you refer to.
>>>>>>
>>>>>> Does my use of a single static variable that holds the ongoing
>>>>>> execution
>>>>>> trace by itself necessarily completely disqualify my system from
>>>>>> applying to the halting problem or not?
>>>>>>
>>>>>> a) Yes
>>>>>> b) No
>>>>>
>>>>> Error of the Complex Question, just like the question of "Have you
>>>>> stopped lying about your Halt Decider?".
>>>>>
>>>>> It isn't the existence of a static variable itself that might
>>>>> disqualify
>>>>> your system for applying to the halting problem,
>>>>
>>>> André disagrees so one of you must be wrong.
>>>
>>> Then take his answer and go away as you admit defeat.
>>>
>>
>> That is not how categorically exhaustive reasoning works. Categorically
>> exhaustive reasoning eliminates the possibility of the error of
>> omission. It results in limited subject domain omniscience.
>>
>> It only stops when
>> (1) A solution is found.
>> (2) No solution exist within omniscience.
>
> But your question, as I explained, was not categorically exhaustive.
>

Polar (yes/no) questions only have {yes, no} answers.
{yes,no} completely exhausts the entire category of answers to polar
(yes/no) questions.

> Have you stopped lying about your Halt Decider?

To the best of my knowledge I have only actually lied once in the last
ten years. I lied to a close friend about a very hurtful truth to
protect them from this very hurtful truth.

I do the best that I can to always tell the truth for two reasons:
(1) I have a very deep passion for mathematically formalizing the notion
of analytical truth and this is the sole reason why I pursue:
(a) The Halting Problem
(b) Gödel's 1931 incompleteness theorem
(c) The Tarski Undefinability theorem
(d) The Liar Paradox

(2) I honestly believe that people intentionally spreading dangerous
lies such as 2020 election fraud and covid-19 disinformation may be
eternally incinerated:


Click here to read the complete article
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From: NoO...@NoWhere.com (olcott)
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 by: olcott - Sat, 18 Sep 2021 22:15 UTC

On 9/18/2021 5:08 PM, André G. Isaak wrote:
> On 2021-09-18 14:55, olcott wrote:
>> On 9/18/2021 3:45 PM, Richard Damon wrote:
>>> On 9/18/21 4:17 PM, olcott wrote:
>>>> On 9/18/2021 2:57 PM, Richard Damon wrote:
>>>>> On 9/18/21 3:39 PM, olcott wrote:
>>>>>> On 9/18/2021 2:24 PM, Richard Damon wrote:
>>>>>>> On 9/18/21 1:08 PM, olcott wrote:
>>>>>>>> On 9/18/2021 11:52 AM, André G. Isaak wrote:
>>>>>>>>> On 2021-09-18 10:39, olcott wrote:
>>>>>>>>>> On 9/18/2021 11:10 AM, André G. Isaak wrote:
>>>>>>>>>>> On 2021-09-18 09:17, olcott wrote:
>>>>>>>>>>>> On 9/18/2021 10:04 AM, André G. Isaak wrote:
>>>>>>>>>>>>> On 2021-09-18 07:57, olcott wrote:
>>>>>>>>>>>>>
>>>>>>>>>>>>>> I either must stick with C/x86 code or write a RASP
>>>>>>>>>>>>>> machine, the
>>>>>>>>>>>>>> only way that my key insights can possible be fully
>>>>>>>>>>>>>> understood is
>>>>>>>>>>>>>> to have every single detail as fully operational code such
>>>>>>>>>>>>>> that
>>>>>>>>>>>>>> we can simply see what it does and thus not merely imagine
>>>>>>>>>>>>>> what
>>>>>>>>>>>>>> it would do.
>>>>>>>>>>>>>
>>>>>>>>>>>>> Why do you insist on continuously repeating this rather
>>>>>>>>>>>>> ridiculous
>>>>>>>>>>>>> claim?
>>>>>>>>>>>>>
>>>>>>>>>>>>> When working with Turing Machines one doesn't need to 'merely
>>>>>>>>>>>>> imagine what it would do.' One can see *exactly* what it does.
>>>>>>>>>>>>>
>>>>>>>>>>>>> André
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> When H is defined as a simulating halt decider then H correctly
>>>>>>>>>>>> decides the halt status of ⟨Ĥ⟩ ⟨Ĥ⟩.
>>>>>>>>>>>
>>>>>>>>>>> And this statement relates to my post how exactly?
>>>>>>>>>>>
>>>>>>>>>>> André
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> How can [One can see *exactly* what it does] show that my
>>>>>>>>>> claim that
>>>>>>>>>> simulating halt decider H applied to ⟨Ĥ⟩ ⟨Ĥ⟩ does not correctly
>>>>>>>>>> decide the halt status of ⟨Ĥ⟩ ⟨Ĥ⟩ ?
>>>>>>>>>
>>>>>>>>> I made no claims whatsoever in my post about your H.
>>>>>>>>
>>>>>>>> This is exactly what I mean by dishonest dodge AKA the strawman
>>>>>>>> error.
>>>>>>>>
>>>>>>>> When we examine the Peter Linz H applied to ⟨Ĥ⟩ ⟨Ĥ⟩
>>>>>>>>
>>>>>>>> there is nothing in the peter Linz text where
>>>>>>>> [One can see *exactly* what it does]
>>>>>>>>
>>>>>>>> when we assume that the Peter Linz H/Ĥ are based on simulating halt
>>>>>>>> deciders.
>>>>>>>
>>>>>>> In the Linz text, we are not given the detail of what the
>>>>>>> machines do
>>>>>>> inside for their processing, but we know EXACTLY how they behave
>>>>>>> at an
>>>>>>> input/output level.
>>>>>>>
>>>>>>> H is given a defined input, a properly encoded version of H^ (<H^>)
>>>>>>>
>>>>>>> and is defined to end, based on whatever algorithm is inside H to
>>>>>>> end at
>>>>>>> either H.qy or H.qn.
>>>>>>>
>>>>>>> He then defines a machine H^ that is based on a nearly exact copy
>>>>>>> of H,
>>>>>>> with just a minor change in the qy state to make it non-terminal but
>>>>>>> loop, and the add a duplication of the input, so H^ can take as an
>>>>>>> input
>>>>>>> <H^> and then get to the copy of the code of H with <H^> <H^> on the
>>>>>>> tape, which is by definition the encoding of the machine H^(<H^>).
>>>>>>>
>>>>>>> Since it is identical code with identical input, but the property of
>>>>>>> being a Computation, if H(<H^>.<H^>) will end at H.qn, then H^
>>>>>>> will end
>>>>>>> at H^.qn (and then halt) and if H ends at H.qy then H^ will get to
>>>>>>> H^.qy
>>>>>>> (and then loop forever).
>>>>>>>
>>>>>>> Yes, Linz doesn't describe how H is designed to get from H.q0 to
>>>>>>> H.qn or
>>>>>>> H.qy, and that is intentional, as that is specified totally by the
>>>>>>> design of H, and since NOTHING has been assumed about it, no
>>>>>>> possible H
>>>>>>> has been excluded from the reasoning.
>>>>>>>
>>>>>>> Thus, even your simulating halt decider case fits in his model.
>>>>>>>
>>>>>>> Once we know what the provided H will do when given this input,
>>>>>>> we can
>>>>>>> see what the machine that this input represents, and if H said it
>>>>>>> would
>>>>>>> halt, it loops, and if H says it won't halt, it Halts, thus any
>>>>>>> answer H
>>>>>>> gives will be wrong.
>>>>>>>
>>>>>>> The only other posibilities is that H never gets to either H.qn or
>>>>>>> H.qy,
>>>>>>> in which case it has also failed to give the right answer.
>>>>>>>
>>>>>>
>>>>>> That is factually incorrect.
>>>>>> H applied to ⟨Ĥ⟩ ⟨Ĥ⟩ correctly transitions to H.qy.
>>>>>
>>>>> When did you ever claim that H (not H1) ever said that H^(H^) was
>>>>> halting.
>>>>>
>>>>> You can't use H1, as H^ is built on H, if you want to use H1, you need
>>>>> to build the H1^ that calls it to test.
>>>>>
>>>>> Maybe you still don't know what that line means.
>>>>>
>>>>>>
>>>>>> The Linz text does cannot possibly get into sufficient detail to show
>>>>>> how this is not true simply because it is true.
>>>>>>
>>>>>
>>>>> Since your described algorithm for H says that H will declare this
>>>>> input
>>>>> to be non-halting, you are lying to say that this H goes to the
>>>>> terminal
>>>>> state qy.
>>>>>
>>>>> The actual behavior of machine H is determined by the algorithm
>>>>> embedded
>>>>> in it. That algorithm says that <H^> <H^> represents a non-halting
>>>>> computation, therefore H will go to H.qn.
>>>>>
>>>>> Linz says that the H that gives the RIGHT answer for an input that is
>>>>> Halting will go to H.qy, but your H doesn't go there because it is not
>>>>> right.
>>>>>
>>>>> 'Give the right answer' is NOT a valid algorithm for a Turing Machine.
>>>>>
>>>>
>>>> When I refer to H1/H I am referring to my C/x86 code.
>>>> When I refer to H/Ĥ I am referring to the Peter Linz templates.
>>>> You can't seem to keep this straight.
>>>>
>>>>
>>>
>>>
>>> Which means you have something MAJORLY wrong with your argument.
>>>
>>> H1 and H in you C/x86 code are two copies of your decider
>>>
>>> Linz H is the Correct Halting decider that is what you claim is
>>> equivalent of you H
>>>
>>
>> Not any more. Ever since I created H1 that does not have pathological
>> self-reference (two weeks ago?) retaining H that does have
>> pathological self-reference, my H(P,P) is equivalent to the Linz Ĥ.qx
>> ⟨Ĥ⟩.
>>
>> My H1(P,P) is equivalent to the Linz H ⟨Ĥ⟩ ⟨Ĥ⟩.
>> Previosly I had no idea how two different halt deciders would
>> coordinate between themselves so I did not discuss the Linz H ⟨Ĥ⟩ ⟨Ĥ⟩.
> There's something horrendously confused about this.
>
> To the extent that I can actually follow your claims given that you keep
> changing the names of things, here is my current understanding of what
> you have:
>
> You have created a 'Halt Decider' H.
>
> Alongside that, you also have a 'confounding case' P which you claim is
> derived from your H in the same way that Linz derives H_Hat from H (It
> isn't actually, but let's not worry about that for now).
>
> You also have a second Halt Decider H1 which is the same as H except
> that it 'does not have pathological self-reference'. You've never shown
> *any* code for this H1, but my assumption is that it is simply a copy of
> H, but since H1 resides at a distinct machine address from H, if H is
> called from within H1 it won't be seen as a recursive call.
>
> The problem here is that Linz's proof asserts that for any putative halt
> decider H, we can construct a new Turing Machine H_Hat which H will be
> unable to decide.
>
> Your H cannot correctly decide H(P, P). You seem to acknowledge this.
>
> Your H1 according to you *can* correctly decide H1(P, P).
>
> But your P isn't derived from your H1. It is derived from your H.
> Alongside your H1 there will be a P1 such that H1(P1, P1) will not be
> correctly decided, so you still aren't overcoming Linz.
>
> Linz doesn't claim that it is impossible for the halting status of
> H_Hat(H_Hat) to be decided. He claims only that it cannot correctly be
> decided by H.
>
> Basically (subject to seeing your actual code), you have a machine H
> which cannot correctly decide whether P(P) halts but which can correctly
> decide whether P1(P1) halts. You also have a machine H1 which can
> correctly decide whether P(P) halts but which cannot correctly decide
> whether P1(P1) halts. So neither of these can possibly count as a
> universal halt decider since each has a case it cannot decide. Neither
> your H nor your H1 can decide the corresponding case described by the
> Linz Proof.
>
> André
>


Click here to read the complete article
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: NoO...@NoWhere.com (olcott)
Date: Sat, 18 Sep 2021 22:32:07 -0500
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 by: olcott - Sun, 19 Sep 2021 03:32 UTC

On 9/18/2021 6:09 PM, Richard Damon wrote:
> On 9/18/21 6:58 PM, olcott wrote:
>> On 9/18/2021 5:55 PM, André G. Isaak wrote:
>>> On 2021-09-18 16:32, olcott wrote:
>>>> On 9/18/2021 5:28 PM, André G. Isaak wrote:
>>>>> On 2021-09-18 16:15, olcott wrote:
>>>>>> On 9/18/2021 5:08 PM, André G. Isaak wrote:
>>>>>
>>>>>>> Basically (subject to seeing your actual code), you have a machine
>>>>>>> H which cannot correctly decide whether P(P) halts but which can
>>>>>>> correctly decide whether P1(P1) halts. You also have a machine H1
>>>>>>> which can correctly decide whether P(P) halts but which cannot
>>>>>>> correctly decide whether P1(P1) halts. So neither of these can
>>>>>>> possibly count as a universal halt decider since each has a case
>>>>>>> it cannot decide. Neither your H nor your H1 can decide the
>>>>>>> corresponding case described by the Linz Proof.
>>>>>>>
>>>>>>> André
>>>>>>>
>>>>>>
>>>>>> By using the H1/H pair we have a universal halt decider.
>>>>>> Whenever they don't provide the same result then one of them is wrong.
>>>>>
>>>>> And since you have no idea *which* one of them is wrong, how exactly
>>>>> is it that you have a 'universal halt decider'?
>>>>>
>>>>> André
>>>>>
>>>>>
>>>>
>>>> I just defeated Rice's theorem, the other details are for another day.
>>>
>>> How exactly have you managed to do that?
>>>
>>
>> I already told you. I wish you would pay attention.
>>
>> int main()
>> {
>>   if (H1((u32)P, (u32)P) != H((u32)P, (u32)P))
>>     OutputString("Pathological self-reference error!");
>> }
>>
>>
>
> Which itself proves nothing.
>
> What is the precise Semantic Property that you are deciding on.
>
> Also, Rice's theorem requires a Decider to give the answer, so an if in
> main isn't the decider that disproves Rice.
>
> Define your property precisely enough that others can verify it.
>
> Define a decider (maybe call it R) that decides that property on a
> machine given to it.
>
> My first guess is that you mean R to be:
>
> u32 R(u32 P) {
> return H1(P,P) != H(P,P);
> }
>
> but now you have to specify what semantic property of P it is detecting.
>

As I have been saying since at least 2004:
As I have been saying since at least 2004:
As I have been saying since at least 2004:
As I have been saying since at least 2004:

The input has the exact same error as the Liar Paradox

[Halting Problem Final Conclusion]
comp.theory
Peter Olcott
Sep 5, 2004, 11:21:57 AM

The Liar Paradox can be shown to be nothing more than
a incorrectly formed statement because of its pathological
self-reference. The Halting Problem can only exist because
of this same sort of pathological self-reference.
https://groups.google.com/g/comp.theory/c/RO9Z9eCabeE/m/Ka8-xS2rdEEJ

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));
}

--
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?[ decidability decider citation ]

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Subject: Re: Why do theory of computation problems require pure functions?[ decidability decider citation ]
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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$1@dont-email.me> <XbOdnZbe3JqE8tv8nZ2dnUU7-emdnZ2d@giganews.com> <4lu1J.13876$Im6.4952@fx09.iad> <x8CdnXa9leSnMtv8nZ2dnUU7-RHNnZ2d@giganews.com> <si6d74$tv6$1@dont-email.me> <si6dp3$7u1$1@dont-email.me> <Nt6dnbjHeOVBW9v8nZ2dnUU7-a3NnZ2d@giganews.com> <si6jmq$er3$1@dont-email.me>
From: NoO...@NoWhere.com (olcott)
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 by: olcott - Sun, 19 Sep 2021 11:56 UTC

On 9/19/2021 1:00 AM, André G. Isaak wrote:
> On 2021-09-18 23:12, olcott wrote:
>> On 9/18/2021 11:19 PM, André G. Isaak wrote:
>>> On 2021-09-18 22:10, André G. Isaak wrote:
>>>
>>>> And note that Rice is talking about properties of Turing Machines
>>>> (or, more properly, of the language accepted by a TM), not
>>>> computations.
>>>
>>> I realized immediately after hitting 'send' that the above will no
>>> doubt confuse you since people have been telling you that Turing
>>> Machines can only express computations whereas C/x86 aren't thus
>>> constrained.
>>>
>>> A computation is a Turing Machine description PLUS an input string.
>>>
>>> Rice's theorem is concerned with the Turing Machine's themselves.
>>>
>>> The Linz proof shows that you cannot construct a halting decider,
>>> i.e. a decider which correctly determines for any given TM + input
>>> string pair, whether that pair represents a halting computation.
>>>
>>> Rice's theorem, on the other hand, would rule out the construction of
>>> something like a Decider Decider, i.e. a TM which takes as its input
>>> a TM description and determines whether that TM qualifies as a
>>> decider, i.e. is guaranteed to halt on *any* possible input.
>>>
>>> André
>>>
>>
>> Bingo! I have said it this same way recently.
>
> No, you have not.

On 9/9/2021 10:25 AM, olcott wrote:
> It is the case that H(P,P)==0 is correct
> It is the case that H1((P,P)==1 is correct
> It is the case the this is inconsistent.
> It is the case that this inconsistency defines a

> decidability decider that correctly rejects P on
> the basis that P has the
> pathological self-reference(Olcott 2004) error.

> decidability decider that correctly rejects P on
> the basis that P has the
> pathological self-reference(Olcott 2004) error.

> decidability decider that correctly rejects P on
> the basis that P has the
> pathological self-reference(Olcott 2004) error.

>
>> // Decidability Decider
>> u32 PSR_Olcott_2004(u32 P)
>> {
>>    return H1(P,P) == H(P,P);
>> }
>
> And how is the above related to anything I wrote in my original post or
> in the post clarifying that post to which you are responding? You don't
> answer the actual question which was asked (i.e. which semantic property
> do you claim to be able to decide using the above?) nor do you show even
> the remotest evidence of having even read my post.
>
> 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? [ PSR error]

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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 11:39:25 -0500
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 by: olcott - Sun, 19 Sep 2021 16:39 UTC

On 9/19/2021 11:11 AM, André G. Isaak wrote:
> On 2021-09-19 09:46, olcott wrote:
>> On 9/19/2021 10:40 AM, André G. Isaak wrote:
>>> On 2021-09-19 08:34, olcott wrote:
>>>> On 9/18/2021 11:19 PM, André G. Isaak wrote:
>>>>> On 2021-09-18 22:10, André G. Isaak wrote:
>>>>>
>>>>>> And note that Rice is talking about properties of Turing Machines
>>>>>> (or, more properly, of the language accepted by a TM), not
>>>>>> computations.
>>>>>
>>>>> I realized immediately after hitting 'send' that the above will no
>>>>> doubt confuse you since people have been telling you that Turing
>>>>> Machines can only express computations whereas C/x86 aren't thus
>>>>> constrained.
>>>>>
>>>>> A computation is a Turing Machine description PLUS an input string.
>>>>>
>>>>> Rice's theorem is concerned with the Turing Machine's themselves.
>>>>>
>>>>> The Linz proof shows that you cannot construct a halting decider,
>>>>> i.e. a decider which correctly determines for any given TM + input
>>>>> string pair, whether that pair represents a halting computation.
>>>>>
>>>>> Rice's theorem, on the other hand, would rule out the construction
>>>>> of something like a Decider Decider, i.e. a TM which takes as its
>>>>> input a TM description and determines whether that TM qualifies as
>>>>> a decider, i.e. is guaranteed to halt on *any* possible input.
>>>>>
>>>>> André
>>>>>
>>>>
>>>> Here is where I referred to my code defining a
>>>> a decidability decider nine days before you did:
>>>
>>> Where did I define or even mention a 'decidability decider'? Above I
>>> discussed (but did not define) a DECIDER decider, i.e. a TM which
>>> determines whether another TM qualifies as a decider.
>>>
>>>> On 9/9/2021 10:25 AM, olcott wrote:
>>>>  > It is the case that H(P,P)==0 is correct
>>>>  > It is the case that H1((P,P)==1 is correct
>>>>  > It is the case the this is inconsistent.
>>>>  > It is the case that this inconsistency
>>>>
>>>>  > defines a decidability decider that correctly
>>>>  > defines a decidability decider that correctly
>>>>  > defines a decidability decider that correctly
>>>>
>>>>  > rejects P on the basis that P has the
>>>>  > pathological self-reference(Olcott 2004) error.
>>>
>>> So what exactly is it that the above is deciding? And how does this
>>> relate to Rice? If you want to claim this is somehow related to rice,
>>> you need to identify some semantic property that you claim to be able
>>> to decide.
>>>
>>> André
>>>
>>
>> It is deciding that either H/P or H1/P form the pathological
>> self-reference error(Olcott 2004). As I said in 2004 this is the same
>> error as the Liar Paradox. This means that either H/P or H1/P are not
>> correctly decidable.
>
> The post in which I mentioned a 'decider decider' which you somehow
> misread as 'decidability decider' was intended to clarify a single
> sentence from an earlier post which you entirely ignored. Why don't you
> go back and actually read that earlier post and address the points made
> therein.
>
> Your ill-defined notion of a 'pathological self-reference error' doesn't
> appear to be a property of a Turing Machine, which is what Rice's
> theorem is concerned with. To the extent that it is a property at all,
> it appears to be a property of specific computations, so this has
> absolutely no relevance to Rice.
>
> André
>

It is the property of H(P,P).

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

Decides that H(P,P) cannot correctly decide the halt status of its
input, thus a semantic property of H relative to P.

The Liar Paradox works this same way.
"This sentence is not true."
When it refers to itself it has the pathological self-reference
error(Olcott 2004).

This is the same as H(P,P) where the input to H refers to H.

When we transform the Liar Paradox so that it does not refer to itself

This sentence is not true: "2 + 3 = 7" then the pathological
self-reference error(Olcott 2004) is eliminated.

The same thing occurs with H1(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? [ PSR error]

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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 12:07:25 -0500
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 by: olcott - Sun, 19 Sep 2021 17:07 UTC

On 9/19/2021 11:56 AM, André G. Isaak wrote:
> On 2021-09-19 10:39, olcott wrote:
>> On 9/19/2021 11:11 AM, André G. Isaak wrote:
>>> On 2021-09-19 09:46, olcott wrote:
>>>> On 9/19/2021 10:40 AM, André G. Isaak wrote:
>>>>> On 2021-09-19 08:34, olcott wrote:
>>>>>> On 9/18/2021 11:19 PM, André G. Isaak wrote:
>>>>>>> On 2021-09-18 22:10, André G. Isaak wrote:
>>>>>>>
>>>>>>>> And note that Rice is talking about properties of Turing
>>>>>>>> Machines (or, more properly, of the language accepted by a TM),
>>>>>>>> not computations.
>>>>>>>
>>>>>>> I realized immediately after hitting 'send' that the above will
>>>>>>> no doubt confuse you since people have been telling you that
>>>>>>> Turing Machines can only express computations whereas C/x86
>>>>>>> aren't thus constrained.
>>>>>>>
>>>>>>> A computation is a Turing Machine description PLUS an input string.
>>>>>>>
>>>>>>> Rice's theorem is concerned with the Turing Machine's themselves.
>>>>>>>
>>>>>>> The Linz proof shows that you cannot construct a halting decider,
>>>>>>> i.e. a decider which correctly determines for any given TM +
>>>>>>> input string pair, whether that pair represents a halting
>>>>>>> computation.
>>>>>>>
>>>>>>> Rice's theorem, on the other hand, would rule out the
>>>>>>> construction of something like a Decider Decider, i.e. a TM which
>>>>>>> takes as its input a TM description and determines whether that
>>>>>>> TM qualifies as a decider, i.e. is guaranteed to halt on *any*
>>>>>>> possible input.
>>>>>>>
>>>>>>> André
>>>>>>>
>>>>>>
>>>>>> Here is where I referred to my code defining a
>>>>>> a decidability decider nine days before you did:
>>>>>
>>>>> Where did I define or even mention a 'decidability decider'? Above
>>>>> I discussed (but did not define) a DECIDER decider, i.e. a TM which
>>>>> determines whether another TM qualifies as a decider.
>>>>>
>>>>>> On 9/9/2021 10:25 AM, olcott wrote:
>>>>>>  > It is the case that H(P,P)==0 is correct
>>>>>>  > It is the case that H1((P,P)==1 is correct
>>>>>>  > It is the case the this is inconsistent.
>>>>>>  > It is the case that this inconsistency
>>>>>>
>>>>>>  > defines a decidability decider that correctly
>>>>>>  > defines a decidability decider that correctly
>>>>>>  > defines a decidability decider that correctly
>>>>>>
>>>>>>  > rejects P on the basis that P has the
>>>>>>  > pathological self-reference(Olcott 2004) error.
>>>>>
>>>>> So what exactly is it that the above is deciding? And how does this
>>>>> relate to Rice? If you want to claim this is somehow related to
>>>>> rice, you need to identify some semantic property that you claim to
>>>>> be able to decide.
>>>>>
>>>>> André
>>>>>
>>>>
>>>> It is deciding that either H/P or H1/P form the pathological
>>>> self-reference error(Olcott 2004). As I said in 2004 this is the
>>>> same error as the Liar Paradox. This means that either H/P or H1/P
>>>> are not correctly decidable.
>>>
>>> The post in which I mentioned a 'decider decider' which you somehow
>>> misread as 'decidability decider' was intended to clarify a single
>>> sentence from an earlier post which you entirely ignored. Why don't
>>> you go back and actually read that earlier post and address the
>>> points made therein.
>>>
>>> Your ill-defined notion of a 'pathological self-reference error'
>>> doesn't appear to be a property of a Turing Machine, which is what
>>> Rice's theorem is concerned with. To the extent that it is a property
>>> at all, it appears to be a property of specific computations, so this
>>> has absolutely no relevance to Rice.
>>>
>>> André
>>>
>>
>> It is the property of H(P,P).
>
> Right, which means this is entirely irrelevant to Rice's theorem.
>

Many historical posts in comp.theory say otherwise.
If a function can be provided that correctly decides that a specific TM
cannot correctly decide a specific input pair (according to many
historical posts on comp.theory) this does refute Rice's theorem.

>> u32 PSR_Olcott_2004(u32 P)
>> {
>>    return H1(P,P) != H(P,P);
>> }
>>
>> Decides that H(P,P) cannot correctly decide the halt status of its input,
>
>
> No, it does not. It decides that the results of H1(P, P) doesn't match
> the results of H(P, P). It 'decides' that one of these is correct and
> the other is not but it cannot tell you which one, which means it can't
> decide whether H(P, P) can correctly decide the halt status of its input.
>

I simply have not gotten to that part yet.

>> thus a semantic property of H relative to P.
>
> That's not a property (semantic or otherwise) of *either* P or H.
>
>> The Liar Paradox works this same way.
>
> The liar's paradox is completely irrelevant to Linz.
>
> André
>

The pathological self-reference error (Olcott 2004) is specifically
relevant to:
(a) The Halting Theorem
(b) The 1931 Incompleteness Theorem
(c) The Tarski undefinability theorem
(d) The Liar Paradox (upon which (c) is based).

--
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? [ PSR error]

<si7seg$uq7$1@dont-email.me>

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https://www.novabbs.com/computers/article-flat.php?id=7379&group=comp.ai.philosophy#7379

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From: jbb...@notatt.com (Jeff Barnett)
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Subject: Re: Why do theory of computation problems require pure functions? [
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 by: Jeff Barnett - Sun, 19 Sep 2021 17:36 UTC

On 9/19/2021 11:07 AM, olcott wrote:
> The pathological self-reference error (Olcott 2004) is specifically
> relevant to:
> (a) The Halting Theorem
> (b) The 1931 Incompleteness Theorem
> (c) The Tarski undefinability theorem
> (d) The Liar Paradox (upon which (c) is based).

Nothing you have done in the past two decades seems to be relevant to
anything. Seems? Just being polite. Actually, why bother: Nothing you
have done in the past two decades is relevant to anything. How long has
your illness made your brain dysfunctional? Friendly reminders: don't
get ahead of yourself; take your meds, all of them.

There are only two paths to long lasting fame for yourself: The first is
to write the USENET version of "The Trisectors" by Underwood Duddley.
The second is to collect two decades of your idiotic newsgroup threads
and turn them into a classic entitled "How to Go Directly from Stark
Personal Depression to Being a World Class Self-Deluded Troll Without
Missing a Meal."

The latter suggestion would be enhanced if you could put your
publication in an academic series with "How To Go Directly Into Solo Law
Practice Without Missing a Meal" by Gerald M. Singer (an LA lawyer).
Fame and notoriety all based on your original works awaits you. And now
we see how all those clever copyright annotations are going to pay off
with big bucks.
--
Jeff Barnett

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

<q5KdnWcPfprt5Nr8nZ2dnUU7-TPNnZ2d@giganews.com>

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From: NoO...@NoWhere.com (olcott)
Date: Sun, 19 Sep 2021 12:54:55 -0500
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 by: olcott - Sun, 19 Sep 2021 17:54 UTC

On 9/19/2021 12:25 PM, André G. Isaak wrote:
> On 2021-09-19 11:07, olcott wrote:
>> On 9/19/2021 11:56 AM, André G. Isaak wrote:
>>> On 2021-09-19 10:39, olcott wrote:
>>>> On 9/19/2021 11:11 AM, André G. Isaak wrote:
>>>>> On 2021-09-19 09:46, olcott wrote:
>>>>>> On 9/19/2021 10:40 AM, André G. Isaak wrote:
>>>>>>> On 2021-09-19 08:34, olcott wrote:
>>>>>>>> On 9/18/2021 11:19 PM, André G. Isaak wrote:
>>>>>>>>> On 2021-09-18 22:10, André G. Isaak wrote:
>>>>>>>>>
>>>>>>>>>> And note that Rice is talking about properties of Turing
>>>>>>>>>> Machines (or, more properly, of the language accepted by a
>>>>>>>>>> TM), not computations.
>>>>>>>>>
>>>>>>>>> I realized immediately after hitting 'send' that the above will
>>>>>>>>> no doubt confuse you since people have been telling you that
>>>>>>>>> Turing Machines can only express computations whereas C/x86
>>>>>>>>> aren't thus constrained.
>>>>>>>>>
>>>>>>>>> A computation is a Turing Machine description PLUS an input
>>>>>>>>> string.
>>>>>>>>>
>>>>>>>>> Rice's theorem is concerned with the Turing Machine's themselves.
>>>>>>>>>
>>>>>>>>> The Linz proof shows that you cannot construct a halting
>>>>>>>>> decider, i.e. a decider which correctly determines for any
>>>>>>>>> given TM + input string pair, whether that pair represents a
>>>>>>>>> halting computation.
>>>>>>>>>
>>>>>>>>> Rice's theorem, on the other hand, would rule out the
>>>>>>>>> construction of something like a Decider Decider, i.e. a TM
>>>>>>>>> which takes as its input a TM description and determines
>>>>>>>>> whether that TM qualifies as a decider, i.e. is guaranteed to
>>>>>>>>> halt on *any* possible input.
>>>>>>>>>
>>>>>>>>> André
>>>>>>>>>
>>>>>>>>
>>>>>>>> Here is where I referred to my code defining a
>>>>>>>> a decidability decider nine days before you did:
>>>>>>>
>>>>>>> Where did I define or even mention a 'decidability decider'?
>>>>>>> Above I discussed (but did not define) a DECIDER decider, i.e. a
>>>>>>> TM which determines whether another TM qualifies as a decider.
>>>>>>>
>>>>>>>> On 9/9/2021 10:25 AM, olcott wrote:
>>>>>>>>  > It is the case that H(P,P)==0 is correct
>>>>>>>>  > It is the case that H1((P,P)==1 is correct
>>>>>>>>  > It is the case the this is inconsistent.
>>>>>>>>  > It is the case that this inconsistency
>>>>>>>>
>>>>>>>>  > defines a decidability decider that correctly
>>>>>>>>  > defines a decidability decider that correctly
>>>>>>>>  > defines a decidability decider that correctly
>>>>>>>>
>>>>>>>>  > rejects P on the basis that P has the
>>>>>>>>  > pathological self-reference(Olcott 2004) error.
>>>>>>>
>>>>>>> So what exactly is it that the above is deciding? And how does
>>>>>>> this relate to Rice? If you want to claim this is somehow related
>>>>>>> to rice, you need to identify some semantic property that you
>>>>>>> claim to be able to decide.
>>>>>>>
>>>>>>> André
>>>>>>>
>>>>>>
>>>>>> It is deciding that either H/P or H1/P form the pathological
>>>>>> self-reference error(Olcott 2004). As I said in 2004 this is the
>>>>>> same error as the Liar Paradox. This means that either H/P or H1/P
>>>>>> are not correctly decidable.
>>>>>
>>>>> The post in which I mentioned a 'decider decider' which you somehow
>>>>> misread as 'decidability decider' was intended to clarify a single
>>>>> sentence from an earlier post which you entirely ignored. Why don't
>>>>> you go back and actually read that earlier post and address the
>>>>> points made therein.
>>>>>
>>>>> Your ill-defined notion of a 'pathological self-reference error'
>>>>> doesn't appear to be a property of a Turing Machine, which is what
>>>>> Rice's theorem is concerned with. To the extent that it is a
>>>>> property at all, it appears to be a property of specific
>>>>> computations, so this has absolutely no relevance to Rice.
>>>>>
>>>>> André
>>>>>
>>>>
>>>> It is the property of H(P,P).
>>>
>>> Right, which means this is entirely irrelevant to Rice's theorem.
>>>
>>
>> Many historical posts in comp.theory say otherwise.
>> If a function can be provided that correctly decides that a specific
>> TM cannot correctly decide a specific input pair (according to many
>> historical posts on comp.theory) this does refute Rice's theorem.
>
> So what is the semantic property *of P* that you claim your
> PSR_Olcott_2004 is capable of identifying?
>
> You can't claim that there is anything 'erroneous' about P. There isn't.
>
> The fact that you run into a problem when you pass a description of P to
> some *other* TM is not an indicator that there is something wrong with
> P. That's like saying that the expression 40 + 50 is 'erroneous' because
> I can't pass it as an argument to tangent().
>
>>>> u32 PSR_Olcott_2004(u32 P)
>>>> {
>>>>    return H1(P,P) != H(P,P);
>>>> }
>>>>
>>>> Decides that H(P,P) cannot correctly decide the halt status of its
>>>> input,
>>>
>>>
>>> No, it does not. It decides that the results of H1(P, P) doesn't
>>> match the results of H(P, P). It 'decides' that one of these is
>>> correct and the other is not but it cannot tell you which one, which
>>> means it can't decide whether H(P, P) can correctly decide the halt
>>> status of its input.
>>>
>>
>> I simply have not gotten to that part yet.
>
> And yet you claimed to be able to 'decide' that H(P, P) cannot correctly
> decide the halt status of its input. Until you actually 'get to that
> part' you have no business making such a claim.
>

Odd man out:
When H1(P,P) != H(P,P) we test
HX(P,P) != H1(P,P)
HX(P,P) != H(P,P)

The one that HX(P,P) agrees with is the correct one.

>>>> thus a semantic property of H relative to P.
>>>
>>> That's not a property (semantic or otherwise) of *either* P or H.
>>>
>>>> The Liar Paradox works this same way.
>>>
>>> The liar's paradox is completely irrelevant to Linz.
>>>
>>> André
>>>
>>
>> The pathological self-reference error (Olcott 2004) is specifically
>> relevant to:
>> (a) The Halting Theorem
>> (b) The 1931 Incompleteness Theorem
>> (c) The Tarski undefinability theorem
>> (d) The Liar Paradox (upon which (c) is based).
>
> So why don't you:
>
> (a) provide a proper definition of "pathological self-reference error"
>     That means a definition which will allow one to unambiguosly
> determine whether an arbitrary expression/entity has this error.

I just provided a reference to function that correctly decide this.
As long as my "pure function of its inputs" becomes fully validated
I will be able to provide the actual source-code that makes this decision.

> (b) explain in what sense an "error" is a property.
> (c) demonstrate that whatever property you are referring to is a
> *semantic* property.
>
> André
>


Click here to read the complete article
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,comp.ai.philosophy,sci.logic,sci.math
References: <a7WdnftR4JAUzNj8nZ2dnUU7-d_NnZ2d@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$1@dont-email.me> <XbOdnZbe3JqE8tv8nZ2dnUU7-emdnZ2d@giganews.com> <4lu1J.13876$Im6.4952@fx09.iad> <x8CdnXa9leSnMtv8nZ2dnUU7-RHNnZ2d@giganews.com> <si6d74$tv6$1@dont-email.me> <si6dp3$7u1$1@dont-email.me> <kZadne336bvC19r8nZ2dnUU7-L_NnZ2d@giganews.com> <si7lli$n28$1@dont-email.me> <ZLidnRFCjJnaxtr8nZ2dnUU7-KXNnZ2d@giganews.com> <si7ng8$s7c$1@dont-email.me> <n5GdnTqFUbEg-tr8nZ2dnUU7-c3NnZ2d@giganews.com> <si7q37$gbh$1@dont-email.me> <BK6dnbrUf-_Q89r8nZ2dnUU7-YnNnZ2d@giganews.com> <si7rq1$i84$1@dont-email.me> <q5KdnWcPfprt5Nr8nZ2dnUU7-TPNnZ2d@giganews.com> <si7v9e$o2e$1@dont-email.me>
From: NoO...@NoWhere.com (olcott)
Date: Sun, 19 Sep 2021 13:33:41 -0500
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 by: olcott - Sun, 19 Sep 2021 18:33 UTC

On 9/19/2021 1:24 PM, André G. Isaak wrote:
> On 2021-09-19 11:54, olcott wrote:
>> On 9/19/2021 12:25 PM, André G. Isaak wrote:
>>> On 2021-09-19 11:07, olcott wrote:
>>>> On 9/19/2021 11:56 AM, André G. Isaak wrote:
>>>>> On 2021-09-19 10:39, olcott wrote:
>>>>>> On 9/19/2021 11:11 AM, André G. Isaak wrote:
>>>>>>> On 2021-09-19 09:46, olcott wrote:
>>>>>>>> On 9/19/2021 10:40 AM, André G. Isaak wrote:
>>>>>>>>> On 2021-09-19 08:34, olcott wrote:
>>>>>>>>>> On 9/18/2021 11:19 PM, André G. Isaak wrote:
>>>>>>>>>>> On 2021-09-18 22:10, André G. Isaak wrote:
>>>>>>>>>>>
>>>>>>>>>>>> And note that Rice is talking about properties of Turing
>>>>>>>>>>>> Machines (or, more properly, of the language accepted by a
>>>>>>>>>>>> TM), not computations.
>>>>>>>>>>>
>>>>>>>>>>> I realized immediately after hitting 'send' that the above
>>>>>>>>>>> will no doubt confuse you since people have been telling you
>>>>>>>>>>> that Turing Machines can only express computations whereas
>>>>>>>>>>> C/x86 aren't thus constrained.
>>>>>>>>>>>
>>>>>>>>>>> A computation is a Turing Machine description PLUS an input
>>>>>>>>>>> string.
>>>>>>>>>>>
>>>>>>>>>>> Rice's theorem is concerned with the Turing Machine's
>>>>>>>>>>> themselves.
>>>>>>>>>>>
>>>>>>>>>>> The Linz proof shows that you cannot construct a halting
>>>>>>>>>>> decider, i.e. a decider which correctly determines for any
>>>>>>>>>>> given TM + input string pair, whether that pair represents a
>>>>>>>>>>> halting computation.
>>>>>>>>>>>
>>>>>>>>>>> Rice's theorem, on the other hand, would rule out the
>>>>>>>>>>> construction of something like a Decider Decider, i.e. a TM
>>>>>>>>>>> which takes as its input a TM description and determines
>>>>>>>>>>> whether that TM qualifies as a decider, i.e. is guaranteed to
>>>>>>>>>>> halt on *any* possible input.
>>>>>>>>>>>
>>>>>>>>>>> André
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Here is where I referred to my code defining a
>>>>>>>>>> a decidability decider nine days before you did:
>>>>>>>>>
>>>>>>>>> Where did I define or even mention a 'decidability decider'?
>>>>>>>>> Above I discussed (but did not define) a DECIDER decider, i.e.
>>>>>>>>> a TM which determines whether another TM qualifies as a decider.
>>>>>>>>>
>>>>>>>>>> On 9/9/2021 10:25 AM, olcott wrote:
>>>>>>>>>>  > It is the case that H(P,P)==0 is correct
>>>>>>>>>>  > It is the case that H1((P,P)==1 is correct
>>>>>>>>>>  > It is the case the this is inconsistent.
>>>>>>>>>>  > It is the case that this inconsistency
>>>>>>>>>>
>>>>>>>>>>  > defines a decidability decider that correctly
>>>>>>>>>>  > defines a decidability decider that correctly
>>>>>>>>>>  > defines a decidability decider that correctly
>>>>>>>>>>
>>>>>>>>>>  > rejects P on the basis that P has the
>>>>>>>>>>  > pathological self-reference(Olcott 2004) error.
>>>>>>>>>
>>>>>>>>> So what exactly is it that the above is deciding? And how does
>>>>>>>>> this relate to Rice? If you want to claim this is somehow
>>>>>>>>> related to rice, you need to identify some semantic property
>>>>>>>>> that you claim to be able to decide.
>>>>>>>>>
>>>>>>>>> André
>>>>>>>>>
>>>>>>>>
>>>>>>>> It is deciding that either H/P or H1/P form the pathological
>>>>>>>> self-reference error(Olcott 2004). As I said in 2004 this is the
>>>>>>>> same error as the Liar Paradox. This means that either H/P or
>>>>>>>> H1/P are not correctly decidable.
>>>>>>>
>>>>>>> The post in which I mentioned a 'decider decider' which you
>>>>>>> somehow misread as 'decidability decider' was intended to clarify
>>>>>>> a single sentence from an earlier post which you entirely
>>>>>>> ignored. Why don't you go back and actually read that earlier
>>>>>>> post and address the points made therein.
>>>>>>>
>>>>>>> Your ill-defined notion of a 'pathological self-reference error'
>>>>>>> doesn't appear to be a property of a Turing Machine, which is
>>>>>>> what Rice's theorem is concerned with. To the extent that it is a
>>>>>>> property at all, it appears to be a property of specific
>>>>>>> computations, so this has absolutely no relevance to Rice.
>>>>>>>
>>>>>>> André
>>>>>>>
>>>>>>
>>>>>> It is the property of H(P,P).
>>>>>
>>>>> Right, which means this is entirely irrelevant to Rice's theorem.
>>>>>
>>>>
>>>> Many historical posts in comp.theory say otherwise.
>>>> If a function can be provided that correctly decides that a specific
>>>> TM cannot correctly decide a specific input pair (according to many
>>>> historical posts on comp.theory) this does refute Rice's theorem.
>>>
>>> So what is the semantic property *of P* that you claim your
>>> PSR_Olcott_2004 is capable of identifying?
>>>
>>> You can't claim that there is anything 'erroneous' about P. There isn't.
>>>
>>> The fact that you run into a problem when you pass a description of P
>>> to some *other* TM is not an indicator that there is something wrong
>>> with P. That's like saying that the expression 40 + 50 is 'erroneous'
>>> because I can't pass it as an argument to tangent().
>>>
>>>>>> u32 PSR_Olcott_2004(u32 P)
>>>>>> {
>>>>>>    return H1(P,P) != H(P,P);
>>>>>> }
>>>>>>
>>>>>> Decides that H(P,P) cannot correctly decide the halt status of its
>>>>>> input,
>>>>>
>>>>>
>>>>> No, it does not. It decides that the results of H1(P, P) doesn't
>>>>> match the results of H(P, P). It 'decides' that one of these is
>>>>> correct and the other is not but it cannot tell you which one,
>>>>> which means it can't decide whether H(P, P) can correctly decide
>>>>> the halt status of its input.
>>>>>
>>>>
>>>> I simply have not gotten to that part yet.
>>>
>>> And yet you claimed to be able to 'decide' that H(P, P) cannot
>>> correctly decide the halt status of its input. Until you actually
>>> 'get to that part' you have no business making such a claim.
>>>
>>
>> Odd man out:
>> When H1(P,P) != H(P,P) we test
>>    HX(P,P) != H1(P,P)
>>    HX(P,P) != H(P,P)
>>
>> The one that HX(P,P) agrees with is the correct one.
>
> There are a potentially infinite number of Hns. Your 'decider' only
> qualifies as a decider if it works for *every* one of them. Your 'odd
> man out strategy' only works if the case you are testing happens to be
> among the three which are included in your test function.
>


Click here to read the complete article
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: NoO...@NoWhere.com (olcott)
Date: Mon, 20 Sep 2021 21:35:05 -0500
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 by: olcott - Tue, 21 Sep 2021 02:35 UTC

On 9/20/2021 9:21 PM, Richard Damon wrote:
> On 9/20/21 9:33 PM, olcott wrote:
>> On 9/20/2021 8:28 PM, Richard Damon wrote:
>>> On 9/20/21 7:33 PM, olcott wrote:
>>>> On 9/20/2021 5:06 PM, Ben Bacarisse wrote:
>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>
>>>>>> On 9/20/2021 5:00 AM, Ben Bacarisse wrote:
>>>>>>> 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).
>>>>>>
>>>>>> Unless one of them has a pathological self-reference relationship with
>>>>>> its input and the other one does not.
>>>>>
>>>>> No.  I stated a fact (about TMs) that has no exceptions.  Your secret C
>>>>> code is another matter, of course.  It's just the deception of calling
>>>>> your code a "machine" that I was objecting to.  It gives your hidden
>>>>> code an air of formality that it lacks.
>>>>>
>>>>
>>>> This is easily proven in a way that you are incapable of understanding.
>>>>
>>>> void P(u32 x)
>>>> {
>>>>    if (H(x, x))
>>>>      HERE: goto HERE;
>>>> }
>>>>
>>>> int main()
>>>> {
>>>>    Output("Input_Halts = ", H((u32)P, (u32)P));
>>>>    Output("Input_Halts = ", H1((u32)P, (u32)P));
>>>> }
>>>>
>>>> Line 1 of main() specifies a different computation than line 2 of main()
>>>> even though the source code of H1 is a copy of H.
>>>>
>>>
>>> Right, and since it is a DIFFERENT computation, it doesn't count that it
>>> can decide P.
>>>
>>> It is only the computation that P (really H^) is built on that matters.
>>>
>>> Since H and H1 are different computaitons, H1 doesn't count.
>>>
>>
>> They are only different because of the pathological self reference
>> (self-contradiction) error. All inputs not having this error relative to
>> their halt decider derive identical results for both H and H1.
>>
>
> There is NO 'pathological self reference error' for Turing machines,
> because they CAN'T self reference, only provide copies.
>

Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
if the simulated ⟨Ĥ⟩ applied to ⟨Ĥ⟩ halts, and

Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
if the simulated ⟨Ĥ⟩ applied to ⟨Ĥ⟩ does not halt

Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ does specify infinitely nested simulation to every
simulating halt decider: Ĥ.qx

Ĥ does have its own machine description as its input so
IT IS SELF-REFERENCE

H ⟨Ĥ⟩ ⟨Ĥ⟩ does not specify infinitely nested simulation to any
simulating halt decider: H

H does not have its own machine description as its input so
IT IS NOT SELF-REFERENCE

It doesn't matter what this difference is called, it can even be called
"late for dinner". That this difference exists and causes the behavior
to vary is what needs to be known.

--
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?

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From: NoO...@NoWhere.com (olcott)
Date: Mon, 20 Sep 2021 22:07:02 -0500
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 by: olcott - Tue, 21 Sep 2021 03:07 UTC

On 9/20/2021 9:45 PM, Ben Bacarisse wrote:
> olcott <NoOne@NoWhere.com> writes:
>
>> It doesn't matter what this difference is called, it can even be
>> called "late for dinner". That this difference exists and causes the
>> behavior to vary is what needs to be known.
>
> Either H.q0 <H^><H^> and H^.qx <H^><H^> both transition to their
> respective rejecting states, or H.q0 <H^><H^> transitions to H.qy and
> H^.qx <H^><H^> does not halt. This difference in behaviour is of no
> help to you.
>
> Feel free to quote me. I won't deny having said this next week. If I
> find I'm wrong about it, I'll say so. That's what an honest person
> does. Whether anything /you/ say can be trusted will depend on how you
> respond to other recent posts.
>

The same initial input to a specific partial halt decider instance H
must always consistently derive the same final output is sustained.

That an exact copy of this partial halt decider instance H1 must alway
derive the same results as the original on the same input as the orginal
seems to be refuted.

The only exception to the rule may be when the input invokes one of
these instances and not the other one.

Ĥ applied to ⟨Ĥ⟩ is applied to its own TM description.
H applied to ⟨Ĥ⟩ ⟨Ĥ⟩ is NOT applied to its own TM description.
This makes the two computations distinctly different.

It may be the case that this is the only exception where identical
machines on the same input do not derive identical results.

--
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? [ computation ? ]

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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: Tue, 21 Sep 2021 10:16:12 -0500
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 by: olcott - Tue, 21 Sep 2021 15:16 UTC

On 9/20/2021 11:42 PM, Richard Damon wrote:
> On 9/21/21 12:03 AM, olcott wrote:
>> On 9/20/2021 10:21 PM, Richard Damon wrote:
>>> On 9/20/21 10:25 PM, olcott wrote:
>>>> On 9/20/2021 9:12 PM, Richard Damon wrote:
>>>>> On 9/20/21 8:14 PM, olcott wrote:
>>>>>> On 9/20/2021 7:00 PM, Ben Bacarisse wrote:
>>>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>>>
>>>>>>>> On 9/20/2021 5:06 PM, Ben Bacarisse wrote:
>>>>>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>>>>>
>>>>>>>>>> On 9/20/2021 5:00 AM, Ben Bacarisse wrote:
>>>>>>>>>>> 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).
>>>>>>>>>>
>>>>>>>>>> Unless one of them has a pathological self-reference relationship
>>>>>>>>>> with
>>>>>>>>>> its input and the other one does not.
>>>>>>>>> No.  I stated a fact (about TMs) that has no exceptions.  Your
>>>>>>>>> secret C
>>>>>>>>> code is another matter, of course.  It's just the deception of
>>>>>>>>> calling
>>>>>>>>> your code a "machine" that I was objecting to.  It gives your
>>>>>>>>> hidden
>>>>>>>>> code an air of formality that it lacks.
>>>>>>>>
>>>>>>>> This is easily proven in a way that you are incapable of
>>>>>>>> understanding.
>>>>>>>
>>>>>>> You can't even write English.  Saying "This is easily proven"
>>>>>>> following
>>>>>>> a quote from me that you are wrong, means you can easily prove what I
>>>>>>> said in the quote -- that you are wrong.  That is indeed the case,
>>>>>>> but
>>>>>>> it is unlikely to be what you meant to say.
>>>>>>>
>>>>>>> Your junk functions are not "machines".  The terms suggests an
>>>>>>> undeserved formality.
>>>>>>>
>>>>>>
>>>>>> void P(u32 x)
>>>>>> {
>>>>>>     if (H(x, x))
>>>>>>       HERE: goto HERE;
>>>>>> }
>>>>>>
>>>>>> The actual correct x86 emulation of the input to H1(P,P) is different
>>>>>> than the actual correct x86 emulation of the input to H(P,P).
>>>>>
>>>>> Which means that your emulator is broken, or H isn't a Computation.
>>>>>
>>>>> PERIOD.
>>>>>
>>>>
>>>> That would mean that "a computation" cannot possibly determine that it
>>>> has been invoked in infinitely recursive simulation, whereas a C
>>>> function with a a pair of static local variables can.
>>>>
>>>
>>> Right, it can't
>>>
>>> Yep, a C code fragment can easily be a non-computation.
>>>
>>>> This means that a C function can do something that a TM cannot do thus
>>>> making it strictly more powerful than a TM. Since this seems implausible
>>>> I estimate that you are simply wrong.
>>>
>>> Nope.
>>>
>>> The Rule is that there is no COMPUTATION that the C function can do that
>>> a Turing Machine can not do. This is the definition of Turing
>>> Competeness and the Turing Equivalence rule.
>>>
>>
>> Yes a C function can determine that it has been called in infinitely
>> nested simulation only because it is able to maintain static local data
>> that is not erased between nested simulations.
>>
>> If a TM cannot maintain static data between nested simulations then a TM
>> cannot detect when it is within infinitely nested simulations. This
>> makes the C function strictly more powerful than the TM.
>
> Maybe, but it doesn't mean it can COMPUTE something that a Turing
> Machine can, which is the only thing that Computation Theory is
> concerned with.
>
> If it isn't a pure mapping of an input to an output, Computation Theory
> doesn't care about it.
>
>>
>>> Also, any 'complete' program (or complete fragment) that has a well
>>> defined input, can be expressed as a Computation, and thus a Turing
>>> Machine could do the equivalent of it. The key here is COMPLETE. You
>>> function isn't 'Complete' as exection goes outside of it and then comes
>>> back in.
>>
>> Exactly the same way that the simulation of the
>>
>> machine description of a UTM H that simulates
>> the machine description P the simulates
>>
>> machine description of a UTM H that simulates
>> the machine description P the simulates
>>
>> machine description of a UTM H that simulates
>> the machine description P the simulates ...
>>
>> Olcott H can detect when Olcott P is doing this only because Olcott H
>> has static local data the survives nested simulations.
>>
>> If a TM cannot have such static local data then Olcott H is strictly
>> more powerful than Linz H.
>>
>
>
> Right, if H IS just a UTM, then H^ is non-halting, but then H doesn't
> give an answer to the question H(H^,H^), so it can't answer the question.
>

Although Olcott H can watch the nested simulation of itself because it
has static local data Linz Ĥ could not do this if it is not allowed to
have the equivalent of static local data. This would make Olcott H
strictly more powerful that Linz Ĥ, when Linz Ĥ is arbitrarily forbidden
from having its own static local data.

> Once H has the code to abort the simulation loop, and is also still a

We can get here because the Linz Ĥ cannot even get to the point where
the abort criteria is matched because it is forced to erase the
execution data that would show this.

> Computation, then H^ will no longer be stuck in an infinite recursion as
> the H inside it will ALSO do that same abort to keep it out of the loop,
> and H when coming up with its answer needs to take that into account to
> give the right answer.
>

This never happens. Ĥ must see at least two iterations and without
static local data it can at most only see one.

> The fact that you can write a program that can detect this sort of
> recusion doesn't matter to Computation Theory, it is only concerned
> about actual Computations,

It does not make sense that arbitrary rules would allow a C function to
be strictly more powerful than a TM so you must be wrong.

> and a proper Halt Decider on Computation MUST
> be a Computation, as the behavior of a Computaton only depends on the
> Machine/ALgorithm and the Input Data, so ANY decider that changes its
> answer based on something outside that CAN'T be right, by definition, it
> give two different answers for a question that always has the same
> answer, so it MUST be wrong at time.
>

In the case of Olcott H, H merely provides no answer at all until (1) It
has seen a behavior pattern that proves that its input matches a never
halting behavior pattern (2) Its input halts on its own.

> The key here is that if H isn't a Computation, then the 'machine' H^
> isn't either, so Computation Theory doesn't care about what it does.
>

So a halt decider can be made yet it breaks arbitrary rules so no one
cares that a halt decider can be made.

> The Halting Problem of Computation Theory is STRICTLY about actual
> Computations.
>
> If your H ACTUALLY is a correct decider for ALL Turing Machines, then by
> definition it needs to be actually a Computation for ANY Turing Machine
> given to it, and thus, it can be shown that there does actually exist a
> Turing Machine version of it that can take any Turing Machine as an
> input. Since this Turing Machine version IS actually a Computation, we
> can use the Linz ^ trick on it showing that it gets this case wrong.


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