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computers / comp.ai.philosophy / Re: Concise refutation of halting problem proofs V20

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* Concise refutation of halting problem proofs V20 [ Ben Bacarisse ]olcott
+- Re: Concise refutation of halting problem proofs V20 [ Richard FAILSolcott
`- Re: Concise refutation of halting problem proofs V20olcott

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Concise refutation of halting problem proofs V20 [ Ben Bacarisse ]

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Subject: Concise refutation of halting problem proofs V20 [ Ben Bacarisse ]
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 by: olcott - Sat, 20 Nov 2021 04:43 UTC

#include <stdint.h>
#include <stdio.h>
typedef int (*ptr)();

int H(ptr x, ptr y)
{ x(y); // direct execution of P(P)
return 1;
}

// Minimal essence of Linz(1990) Ĥ
// and Strachey(1965) P
int P(ptr x)
{ H(x, x);
return 1; // Give P a last instruction at the "c" level
}

int main(void)
{ H(P, P);
}

Computation that halts
a computation is said to halt whenever it enters a final state.
(Linz:1990:234)

PSR set: Combinations of H/P having pathological self-reference
For every possible H of H(P,P) invoked from main() where P(P) calls this
same H(P,P) and H simulates or executes its input and aborts or does not
abort its input P never reaches its last instruction.

PSR subset: Because we know that the input to H(P,P) never halts for the
whole PSR set and a subset of these H/P combinations aborts the
execution or simulation of its input then we know that for this entire
subset the input to H(P,P) never halts and H(P,P) halts.

When int main(void) { P(P); } is invoked on H/P elements of the above
PSR subset, then we have a cases where the input to H(P,P) never halts
and P(P) halts.

This conclusively proves when the input to H(P,P) never halts and the
same P(P) does halt that this does not form a contradiction.

Halting problem undecidability and infinitely nested simulation (V2)
November 2021 PL Olcott

https://www.researchgate.net/publication/356105750_Halting_problem_undecidability_and_infinitely_nested_simulation_V2

--
Copyright 2021 Pete Olcott

Talent hits a target no one else can hit;
Genius hits a target no one else can see.
Arthur Schopenhauer

Re: Concise refutation of halting problem proofs V20 [ Richard FAILS ]

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Subject: Re: Concise refutation of halting problem proofs V20 [ Richard FAILS
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 by: olcott - Sun, 21 Nov 2021 00:44 UTC

On 11/20/2021 6:31 PM, Richard Damon wrote:
> On 11/20/21 7:22 PM, olcott wrote:
>> On 11/20/2021 6:04 PM, Richard Damon wrote:
>>> On 11/20/21 6:45 PM, olcott wrote:
>>>> On 11/20/2021 5:34 PM, Richard Damon wrote:
>>>>>
>>>>> On 11/20/21 5:48 PM, olcott wrote:
>>>>>> On 11/20/2021 4:27 PM, Richard Damon wrote:
>>>>>>> On 11/20/21 5:12 PM, olcott wrote:
>>>>>>>> On 11/20/2021 4:06 PM, Richard Damon wrote:
>>>>>>>>> On 11/20/21 4:55 PM, olcott wrote:
>>>>>>>>>> On 11/20/2021 3:42 PM, Richard Damon wrote:
>>>>>>>>>>> On 11/20/21 12:48 PM, olcott wrote:
>>>>>>>>>>>> On 11/20/2021 10:47 AM, Ben Bacarisse wrote:
>>>>>>>>>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>>>>>>>>>
>>>>>>>>>>>>>> On 11/20/2021 4:57 AM, Ben Bacarisse wrote:
>>>>>>>>>>>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>>>>>>>>>>> Subject:
>>>>>>>>>>>>>>> Re: Concise refutation of halting problem proofs V20 [
>>>>>>>>>>>>>>> Ben Bacarisse ]
>>>>>>>>>>>>>>> I would appreciate it if you would not use my name in
>>>>>>>>>>>>>>> connection with
>>>>>>>>>>>>>>> your "work".  Thank you.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> I have finally made it clear that when the input to H(P,P)
>>>>>>>>>>>>>> never halts
>>>>>>>>>>>>>> the fact that (P) halts does not contradict this.
>>>>>>>>>>>>>
>>>>>>>>>>>>> I would appreciate it if you would not use my name in
>>>>>>>>>>>>> connection with
>>>>>>>>>>>>> your "work".  I can't make you, but I trust you have some
>>>>>>>>>>>>> sense of
>>>>>>>>>>>>> propriety.  Thank you.
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> Not in this case. You have only unfairly evaluated my work.
>>>>>>>>>>>> Now is your chance for an accurate review.
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> No, your 'proof' is still a lie based on using the wrong
>>>>>>>>>>> definitions of words.
>>>>>>>>>>>
>>>>>>>>>>> The computation that is the input to H(P,P) WILL halt if
>>>>>>>>>>> H(P,P) returns the value 0 as long as P is the required
>>>>>>>>>>> computation based on that H.
>>>>>>>>>>>
>>>>>>>>>>> FAIL.
>>>>>>>>>>
>>>>>>>>>> Everyone here defines the domain of function H to contain
>>>>>>>>>> elements that are only vague ideas.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> LIE.
>>>>>>>>>
>>>>>>>>>
>>>>>>>>> The Domain of a proper Halt decider is PRECISELY defined.
>>>>>>>>>
>>>>>>>>>> The domain of function H must actually be a set of elements
>>>>>>>>>> that each specify a sequence of configurations.
>>>>>>>>>
>>>>>>>>> And they do.
>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Function H maps elements of its domain D to {0,1}
>>>>>>>>>> Domain D is comprised of elements that specify a sequence of
>>>>>>>>>> configurations.
>>>>>>>>>> H maps elements E of D to {0,1} on the basis of whether or not
>>>>>>>>>> E reaches its final state.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Except that for the Computation P(P)
>>>>>>>>
>>>>>>>> This is the exact vague idea that cannot possibly exist in the
>>>>>>>> domain of H.
>>>>>>>
>>>>>>> This is NOT a 'vague idea', P, which Linz describes as H^, is
>>>>>>> PRECISELY defined in terms of H, which you claim to have a
>>>>>>> definition of.
>>>>>>>
>>>>>>
>>>>>> A specified sequence of configurations can be an element of the
>>>>>> domain of H. Some belief about how P(P) is supposed to behave
>>>>>> cannot be such an element.
>>>>>
>>>>> And what is 'vague' about Linz's description of how to build H^,
>>>>> which you call P.
>>>>
>>>> On 11/20/2021 5:02 PM, Richard Damon wrote:
>>>>  > Remember,the FUNDAMENTAL question being asked of a Halt
>>>>  > Decider is does a given computation, when run independently
>>>>  > Halt or not when run.
>>>>
>>>> When you try and find a way to translate that into an element of the
>>>> domain of function H
>>>>
>>>> YOU FAIL
>>>> YOU FAIL
>>>> YOU FAIL
>>>
>>> LIE.
>>>
>>> Is the domain of H not representations of Computations?
>>
>> The domain of H is sets of specified sequences of configurations that
>> may not be computations. (A computation is defined to halt).
>>
>> It is the subtle difference between representation and specification
>> that causes you to get the wrong answer.
>>
>> There is no mathematically precise way to say this:
>>  > Remember,the FUNDAMENTAL question being asked of a
>>  > Halt Decider is does a given computation, when run
>>  > independently Halt or not when run.
>>
>> There is no way to put [when run independently]
>> into any specified sequence of configurations.
>
> Why not?
>

How do you tell a mathematical function that it is not allowed to base
its halt status decision on the sequence of configurations specified by
(P, I) and instead must base its halt status decision on P(I) [when run
independently] ???

--
Copyright 2021 Pete Olcott

Talent hits a target no one else can hit;
Genius hits a target no one else can see.
Arthur Schopenhauer

Re: Concise refutation of halting problem proofs V20

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 by: olcott - Sun, 21 Nov 2021 00:52 UTC

On 11/20/2021 6:47 PM, André G. Isaak wrote:
> On 2021-11-20 15:12, olcott wrote:
>> On 11/20/2021 4:06 PM, Richard Damon wrote:
>>> On 11/20/21 4:55 PM, olcott wrote:
>>>> On 11/20/2021 3:42 PM, Richard Damon wrote:
>>>>> On 11/20/21 12:48 PM, olcott wrote:
>>>>>> On 11/20/2021 10:47 AM, Ben Bacarisse wrote:
>>>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>>>
>>>>>>>> On 11/20/2021 4:57 AM, Ben Bacarisse wrote:
>>>>>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>>>>> Subject:
>>>>>>>>> Re: Concise refutation of halting problem proofs V20 [ Ben
>>>>>>>>> Bacarisse ]
>>>>>>>>> I would appreciate it if you would not use my name in
>>>>>>>>> connection with
>>>>>>>>> your "work".  Thank you.
>>>>>>>>
>>>>>>>> I have finally made it clear that when the input to H(P,P) never
>>>>>>>> halts
>>>>>>>> the fact that (P) halts does not contradict this.
>>>>>>>
>>>>>>> I would appreciate it if you would not use my name in connection
>>>>>>> with
>>>>>>> your "work".  I can't make you, but I trust you have some sense of
>>>>>>> propriety.  Thank you.
>>>>>>>
>>>>>>
>>>>>> Not in this case. You have only unfairly evaluated my work.
>>>>>> Now is your chance for an accurate review.
>>>>>>
>>>>>
>>>>> No, your 'proof' is still a lie based on using the wrong
>>>>> definitions of words.
>>>>>
>>>>> The computation that is the input to H(P,P) WILL halt if H(P,P)
>>>>> returns the value 0 as long as P is the required computation based
>>>>> on that H.
>>>>>
>>>>> FAIL.
>>>>
>>>> Everyone here defines the domain of function H to contain elements
>>>> that are only vague ideas.
>>>>
>>>
>>> LIE.
>>>
>>>
>>> The Domain of a proper Halt decider is PRECISELY defined.
>>>
>>>> The domain of function H must actually be a set of elements that
>>>> each specify a sequence of configurations.
>>>
>>> And they do.
>>>
>>>>
>>>> Function H maps elements of its domain D to {0,1}
>>>> Domain D is comprised of elements that specify a sequence of
>>>> configurations.
>>>> H maps elements E of D to {0,1} on the basis of whether or not E
>>>> reaches its final state.
>>>>
>>>
>>> Except that for the Computation P(P)
>>
>> This is the exact vague idea that cannot possibly exist in the domain
>> of H.
>>
>> The sequence of configurations specified by the x86 machine language
>> of P is in the domain of H.
>>
>> Some vague idea about what P(P) is supposed to do cannot possibly be
>> in the domain of H.
>
> Which 'vague idea'?
>
> A halt decider doesn't decide what P(P) is "supposed" to do. It decides
> what it actually *does* do when run directly from main. There's nothing
> remotely vague about that.
>
> I think you are confusing the term 'domain' with the term 'scope'. When
> you call P(P) from within H it is within the scope of H. when you
> execute it directly from main it is not within the scope of H. Scope and
> domain are entirely different things.
>
> And a halt decider describes the behaviour of independent computations,
> not of functions called from within the scope of the decider.
>
> André
>

How do you tell a mathematical function that it is not allowed to base
its halt status decision on the sequence of configurations specified by
(P, I) and instead must base its halt status decision on P(I) [when run
independently] ???

--
Copyright 2021 Pete Olcott

Talent hits a target no one else can hit;
Genius hits a target no one else can see.
Arthur Schopenhauer

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