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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory,sci.logic
Subject: =?UTF-8?Q?Re=3A_A_simulating_halt_decider_applied_to_the_The_Peter_?=
 =?UTF-8?Q?Linz_Turing_Machine_description_=E2=9F=A8=C4=A4=E2=9F=A9?=
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On 5/26/2024 6:07 PM, Richard Damon wrote:
> On 5/26/24 6:47 PM, olcott wrote:
>> On 5/26/2024 3:20 PM, Richard Damon wrote:
>>> On 5/26/24 3:14 PM, olcott wrote:
>>>> 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 we see that ⟨Ĥ⟩ ⟨Ĥ⟩ correctly simulated by embedded_H in an
>>>> infinite number of steps cannot possibly reach its own simulated
>>>> final state of ⟨Ĥ.qn⟩ and halt then we correctly deduce that the
>>>> same thing applies when simulating halt decider embedded_H correctly
>>>> simulates less than an infinite number of steps of ⟨Ĥ⟩ ⟨Ĥ⟩.
>>>>
>>>
>>> Nope.
>>>
>>> Since we are talking about Turing Machines, your stipulated POOP 
>>> definitions go away, 
>>
>> https://www.liarparadox.org/Linz_Proof.pdf
>> *Simplified the notation for Ĥ on the top of page three*
>> and put back in the qy state shown in figure 12.2
>>
>> When Ĥ is applied to ⟨Ĥ⟩
>> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
>> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>
>>    Ĥ copies its own Turing machine description: ⟨Ĥ⟩
>>    then invokes embedded_H that simulates ⟨Ĥ⟩ with ⟨Ĥ⟩ as input.
>>
>> It is an easily verified fact that ⟨Ĥ⟩ ⟨Ĥ⟩ correctly simulated by 
>> embedded_H cannot possibly reach its own simulated final state of
>> ⟨Ĥ.qn⟩ in any finite sequence of steps.
> 
> Nope, since we are in Turing Machines, the term "Correctly Simulated" 
> means, and can ONLY mean, the resuts of a UTM simulation, which BY 
> DEFINITION is nopt aborted.

You always seem to make sure respond to a different set of words
than the words I actually said. This could be an honest mistake.

*I SAID A CORRECT SIMULATION OF A FINITE NUMBER OF STEPS*

*WHEN I EXPLICITLY STATE A FINITE NUMBER OF STEPS THEN YOU ARE*
*FLAT OUT WRONG TO SIMPLY ASSUME AN INFINITE NUMBER OF STEPS*

The above is STEP TWO  of my four step proof. STEP ONE can be
discarded if it is easy enough for you and others to accept
this STEP TWO. I already covered most of STEP THREE.

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