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computers / comp.ai.philosophy / Re: Concise refutation of halting problem proofs V22 [ mathematically precise ]

SubjectAuthor
* Concise refutation of halting problem proofs V22 [ precisely definedolcott
`* Re: Concise refutation of halting problem proofs V22 [ mathematicallyolcott
 `- Re: Concise refutation of halting problem proofs V22 [ mathematicallyolcott

1
Concise refutation of halting problem proofs V22 [ precisely defined sets ]

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Subject: Concise refutation of halting problem proofs V22 [ precisely defined
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 by: olcott - Sat, 20 Nov 2021 21:49 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
Every 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
PSR 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 cases where the input to H(P,P) never halts and
P(P) halts. The fact that the input to H(P,P) never halts is not
contradicted by the fact that P(P) halts.

Decidable_PSR subset: The subset of the PSR subset where H returns 0 on
the basis that H correctly detects that P specifies infinite recursion
defines the decidable domain of function H.

Halt decider (Olcott 2021)
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.

The above H could detect that its simulated P is calling H(P,P) with the
same parameters that it was called with, thus specifying infinite
recursion.

Halting problem undecidability and infinitely nested simulation V2

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 V22 [ mathematically precise ]

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 by: olcott - Sun, 21 Nov 2021 00:01 UTC

On 11/20/2021 5:46 PM, Richard Damon wrote:
> On 11/20/21 6:20 PM, olcott wrote:
>> On 11/20/2021 5:02 PM, Richard Damon wrote:
>>> Comment about this being V22 and you version number counting faster
>>> than daily.
>>>
>>> This sort of shows the level of effort (or lack thereof) you are
>>> putting into your logic.
>>>
>>> Basically as soon as someone points our a flaw in your logic, rather
>>> than trying to defend it, you just try to reword you statement to see
>>> if you can find the right 'weasel words' to try to excuse your error,
>>> without even attempting to address the fundamental flaws in your
>>> arguement.
>>>
>>> This basically shows that you DON'T have a defense for what you are
>>> saying.
>>>
>>> Fundamentally, you don't have a shread of ground to stand on as the
>>> problem is that the theory you want to talk about HAS defined the
>>> terms you are trying to mis-use, and you can't get around it.
>>>
>>>
>>> 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
>> YOU FAIL
>
> You Lie, I did it, YOU FAIL.
>
> If the domain of H is NOT representations of Computation then you are
> not talking about a Halt Decider, and thus are one of the biggest liars
> on the planet.

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.

This is mathematically precise:
a specified sequence of configurations reaches the halt state of this
sequence (or not).

--
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 V22 [ mathematically precise ]

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 by: olcott - Sun, 21 Nov 2021 00:38 UTC

On 11/20/2021 6:25 PM, Richard Damon wrote:
> On 11/20/21 7:01 PM, olcott wrote:
>> On 11/20/2021 5:46 PM, Richard Damon wrote:
>>> On 11/20/21 6:20 PM, olcott wrote:
>>>> On 11/20/2021 5:02 PM, Richard Damon wrote:
>>>>> Comment about this being V22 and you version number counting faster
>>>>> than daily.
>>>>>
>>>>> This sort of shows the level of effort (or lack thereof) you are
>>>>> putting into your logic.
>>>>>
>>>>> Basically as soon as someone points our a flaw in your logic,
>>>>> rather than trying to defend it, you just try to reword you
>>>>> statement to see if you can find the right 'weasel words' to try to
>>>>> excuse your error, without even attempting to address the
>>>>> fundamental flaws in your arguement.
>>>>>
>>>>> This basically shows that you DON'T have a defense for what you are
>>>>> saying.
>>>>>
>>>>> Fundamentally, you don't have a shread of ground to stand on as the
>>>>> problem is that the theory you want to talk about HAS defined the
>>>>> terms you are trying to mis-use, and you can't get around it.
>>>>>
>>>>>
>>>>> 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
>>>> YOU FAIL
>>>
>>> You Lie, I did it, YOU FAIL.
>>>
>>> If the domain of H is NOT representations of Computation then you are
>>> not talking about a Halt Decider, and thus are one of the biggest
>>> liars on the planet.
>>
>> 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.
>
> What is mathematically imprecise about that?
>
> Computation P(I) will absolutely EITHER reach a halting state in some
> finite number of steps N, or it will NEVER reach a halting state in an
> unbounded number of steps.
>

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] ???

> Is the problem that you don't understand the concept of unbounded
> numbers or infinities?
>
> If so, Mathematics is NOT a field you should be working in.
>
>>
>> This is mathematically precise:
>> a specified sequence of configurations reaches the halt state of this
>> sequence (or not).
>>
>>
>
> But that isn't the definition of Halting.
>
> Unless the 'specified sequence of configurations' is a UTM applied to
> the input.
>
> That just shows you are not talking about the halting problem because
> you just don't understand what halting is!
>
> Its hard to be convincing about proofs based on 'the meaning of words',
> when you admit that you just don't understand the meaning of a
> fundamental word in the topic.

--
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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