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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: Functions computed by Turing Machines MUST apply finite string
 transformations to inputs --- MT
Date: Sun, 4 May 2025 20:23:05 -0500
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On 5/4/2025 8:04 PM, Ben Bacarisse wrote:
> Mike Terry <news.dead.person.stones@darjeeling.plus.com> writes:
> ...
>> As explained above, UTM(⟨Ĥ⟩ ⟨Ĥ⟩) simulates Ĥ run with input Ĥ (having the
>> same halting behaviour) and Ĥ run with input Ĥ HALTS.  So embedded_H does
>> not "gather enough information to deduce that UTM(⟨Ĥ⟩ ⟨Ĥ⟩) would never
>> halt".  THAT IS JUST A FANTASY THAT YOU HAVE.
>>
>> UTM(⟨Ĥ⟩ ⟨Ĥ⟩) DOES halt, so embedded_H can't possibly gather information
>> that genuinely implies it DOESN'T halt.  The explanation is obvious:
>> embedded_H gathers information that *YOU* believe implies that UTM(⟨Ĥ⟩ ⟨Ĥ⟩)
>> would never halt, but *YOU ARE SIMPLY WRONG*.
> 
> He used to claim that false ("does not halt") was the correct answer,
> /even though/ the computation in question halts!  Those were simpler
> days.  Of course cranks will never admit to having been wrong about
> anything other than a detail or two, so anyone who could be bothered
> could try to get him to retract that old claim.
> 

<MIT Professor Sipser agreed to ONLY these verbatim words 10/13/2022>
     If simulating halt decider H correctly simulates its input D
     until H correctly determines that its simulated D would never
     stop running unless aborted then

     H can abort its simulation of D and correctly report that D
     specifies a non-halting sequence of configurations.
</MIT Professor Sipser agreed to ONLY these verbatim words 10/13/2022>

When Ĥ is applied to ⟨Ĥ⟩
Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn

In other words embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ is correct to
reject its input if

Ĥ.q0 ⟨Ĥ⟩ ⊢* UTM ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
Ĥ.q0 ⟨Ĥ⟩ ⊢* UTM ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
Would not halt.

>> I know you'll not understand what I've just said, because it is all too
>> abstract and you don't understand the concepts involved, and consequently
>> you probably don't agree with my Sipser interpretation, and even if you did
>> I doubt you would be able to work out its consequences.  So I don't expect
>> to be posting any further.
> 
> Not you then!  I sympathise, though my reason for not talking to him is
> his unacceptable insults.
> 


-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer