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computers / comp.ai.philosophy / Re: Concise refutation of halting problem proofs V38 [ Olcott 2021 generic halt deciding principle ]

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* Re: Concise refutation of halting problem proofs V38 [ Olcott 2021olcott
`- Re: Concise refutation of halting problem proofs V38 [ Olcott 2021olcott

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Subject: Re: Concise refutation of halting problem proofs V38 [ Olcott 2021 generic halt deciding principle ]
From: olcott
Newsgroups: comp.theory, comp.ai.philosophy, sci.logic, sci.math
Date: Wed, 8 Dec 2021 21:22 UTC
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From: NoO...@NoWhere.com (olcott)
Subject: Re: Concise refutation of halting problem proofs V38 [ Olcott 2021
generic halt deciding principle ]
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I have reformulated my system so that it correctly handles this.

// Full Linz  Ĥ as C/x86
void P(ptr x)
{
   ptr y = copy(x);
   if (H(x, y))
     HERE: goto HERE;
}

Because it no longer relies on machine addresses H1(P,P) == H(P,P).

[Olcott 2021 generic halt deciding principle] Whenever the pure simulation of the input to simulating halt decider H(x,y) never stops running unless H aborts its simulation H correctly aborts this simulation and returns 0 for not halting.


Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
If the UTM simulation of the input to Ĥ.qx ⟨Ĥ⟩ applied to ⟨Ĥ⟩ reaches its own final state.

Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
If the pure simulation of the input to Ĥqx ⟨Ĥ⟩ ⟨Ĥ⟩ would never reach its final state (whether or not this simulation is aborted) then it is necessarily true that Ĥqx transitions to Ĥ.qn correctly.



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


Subject: Re: Concise refutation of halting problem proofs V38 [ Olcott 2021 generic halt deciding principle ]
From: olcott
Newsgroups: comp.theory, comp.ai.philosophy, sci.logic, sci.math
Date: Wed, 8 Dec 2021 22:40 UTC
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Subject: Re: Concise refutation of halting problem proofs V38 [ Olcott 2021
generic halt deciding principle ]
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<87lf0ulp2g.fsf@bsb.me.uk>
From: NoO...@NoWhere.com (olcott)
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On 12/8/2021 4:16 PM, Ben Bacarisse wrote:
olcott <NoOne@NoWhere.com> writes:

Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
If the UTM simulation...

Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
If the pure simulation...

No.  As you know, the correct annotations for those lines are:

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

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

and the usual conclusion follows immediately form these facts.


Actually even Linz got that incorrectly.
Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ is not deciding whether or not Ĥ (and thus itself) halts it is deciding whether or not ⟨Ĥ⟩ applied to ⟨Ĥ⟩ would halt.

When we further hypothesize the the original H was a simulating halt decider then we get:

Ĥ applied to ⟨Ĥ⟩ essentially specifies infinite recursion that is aborted after the first invocation of this infinite recursion.

Because it is not aborted at the first invocation we get the confusing case where Ĥ halts yet its own simulation of itself must be aborted.

We don't have this issue with H. H applied to ⟨Ĥ⟩ ⟨Ĥ⟩ aborts this infinite recursion at its first invocation.

--
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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