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From: joes <noreply@example.com>
Newsgroups: comp.theory,sci.logic
Subject: Re: A simulating halt decider applied to the The Peter Linz Turing
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Date: Sat, 1 Jun 2024 18:52:09 -0000 (UTC)
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Am Sat, 01 Jun 2024 09:37:01 -0500 schrieb olcott:
> On 6/1/2024 2:52 AM, Mikko wrote:
>> On 2024-05-31 15:35:18 +0000, olcott said:

>>> *A quick summary of the reasoning provided below*
>>> The LHS is behavior that embedded_H is allowed to report on.
>> There is no restrictions on what embedded_H is allowed to report on.
> 
> embedded_H is only allowed to report on the behavior that its finite
> string Turing Machine Description specifies to a UTM.
> 
> embedded_H <is> a UTM except that it stops simulating and reports
> non-halting as soon as it correctly recognizes a non-halting behavior
> pattern that is specified by its input.
"Except". So it is not an UTM.

> When Ĥ is applied to ⟨Ĥ⟩
> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
> 
> (a) Ĥ copies its input ⟨Ĥ⟩
> (b) Ĥ invokes embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩
> (c) embedded_H simulates ⟨Ĥ⟩ ⟨Ĥ⟩
> (d) simulated ⟨Ĥ⟩ copies its input ⟨Ĥ⟩
> (e) simulated ⟨Ĥ⟩ invokes simulated embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩
> (f) simulated embedded_H simulates ⟨Ĥ⟩ ⟨Ĥ⟩
> (g) goto (d)
> 
> embedded_H is not allowed to be applied to Ĥ ⟨Ĥ⟩ because inputs can
> only be finite strings and Ĥ is not a finite string. This means
> that embedded_H is not allowed to report on its own actual behavior.
I can't read that notation. What is H^ and what does it look like?

> embedded_H only allowed to report on the behavior specified by its
> finite string input. That behavior never stops running for 1 to ∞ steps
> of ⟨Ĥ⟩ ⟨Ĥ⟩ correctly simulated by embedded_H.
> 
>> The only reauirement is that embedded_H has the same transition
>> rules as H. Therefore embedded_H reports the same as H, whether
>> allowed or not.
>> 
> Linz H applied to ⟨Ĥ⟩ ⟨Ĥ⟩ derives a different result than
> embedded_H applied to ⟨Ĥ⟩ ⟨Ĥ⟩.
> 
> This is because the in the latter case embedded_H must determine that
> ⟨Ĥ⟩ ⟨Ĥ⟩ correctly simulated by embedded_H cannot possibly stop running
> after 1 to ∞ steps of correct simulation. Thus embedded_H meets its
> abort simulation criteria.
> 
> The former case of Linz H applied to ⟨Ĥ⟩ ⟨Ĥ⟩ can see that embedded_H
> has already aborted its simulation, thus it never reaches its own
> abort criteria.
> 
> It is only because everyone since 1936 has rejected simulation
> OUT-OF-HAND without review that no one ever noticed this before.
> 
>>> The RHS is behavior that embedded_H NOT is allowed to report on.
>>> The LHS and the RHS specify different behaviors.
>> 
>> You have not shown anything with behaviours as LHS and RHS.
>> 
>>> Please to not reply here instead reply at the end of my proof
>>> after all of the steps have been presented.
>> 
>> Not a reasonable request. Correctness of a step of proof does not
>> depend on what follows. If one step is erroneous the rest is
>> irrelevant.
^

-- 
joes