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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory,sci.logic
Subject: Re: Two dozen people were simply wrong --- Try to prove otherwise
Date: Thu, 30 May 2024 20:54:52 -0500
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On 5/30/2024 8:37 PM, Richard Damon wrote:
> On 5/30/24 9:31 AM, olcott wrote:
>> On 5/30/2024 2:40 AM, Mikko wrote:
>>> On 2024-05-30 01:15:21 +0000, olcott said:

>>>> x <is> a finite string Turing machine description that SPECIFIES 
>>>> behavior. The term: "representing" is inaccurate.
>>>
>>> No, x is a description of the Turing machine that specifies the 
>>> behaviour
>>> that H is required to report. 
>>
>> That is what I said.
> 
> Note, the string doesn't DIRECTLY specify behavior, but only indirectly 
> as a description/representation of the Turing Mach
> 

The string directly SPECIFIES behavior to a UTM or to
any TM based on a UTM.

>>
>>> The maning of x is that there is a universal
>>> Turing machine that, when given x and y, simulates what the described
>>> Turing machine does when given y. 
>>
>> Yes that is also correct.
> 
> 
> 
>>
>> When Ĥ is applied to ⟨Ĥ⟩
>> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
>> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>
>> When embedded_H is a UTM then it never halts.
> 
> But it isn't unless H is also a UTM, and then H never returns.
> 
> You like to keep returning to that deception.
> 
>>
>> When embedded_H is a simulating halt decider then its correctly
>> simulated input never reaches its own simulated final state of
>> ⟨Ĥ.qn⟩ and halts. H itself does halt and correctly rejects its
>> input as non-halting.
> 
> Except that isn't what the question is, the question is what the actual 
> behavior of the machine described, or equivalently, the simulation by a 
> REAL UTM (one that never stops till done).

When embedded_H is a real UTM then Ĥ ⟨Ĥ⟩ never stops and embedded_H is
not a decider.

When embedded_H is based on a real UTM then ⟨Ĥ⟩ ⟨Ĥ⟩ correctly simulated
by embedded_H never reaches its own simulated final state of ⟨Ĥ.qn⟩ in
any finite number of steps and after these finite steps embedded_H
halts.

*I am going to stop here and not respond to anything else*
*that you say until AFTER this one point is fully resolved*

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