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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: D correctly simulated by H cannot possibly halt --- templates and
 infinite sets
Date: Fri, 31 May 2024 10:44:22 -0500
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On 5/31/2024 8:10 AM, Mikko wrote:
> On 2024-05-28 16:16:48 +0000, olcott said:
> 
>> typedef int (*ptr)();  // ptr is pointer to int function in C
>> 00       int H(ptr p, ptr i);
>> 01       int D(ptr p)
>> 02       {
>> 03         int Halt_Status = H(p, p);
>> 04         if (Halt_Status)
>> 05           HERE: goto HERE;
>> 06         return Halt_Status;
>> 07       }
>> 08
>> 09       int main()
>> 10       {
>> 11         H(D,D);
>> 12         return 0;
>> 13       }
>>
>> When Ĥ is applied to ⟨Ĥ⟩
>> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
>> Ĥ.q0 ⟨Ĥ⟩ ⊢* embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
>>
>> *Formalizing the Linz Proof structure*
>> ∃H  ∈ Turing_Machines
>> ∀x  ∈ Turing_Machines_Descriptions
>> ∀y  ∈ Finite_Strings
>> such that H(x,y) = Halts(x,x)
>>
>> *Here is the same thing applied to H/D pairs*
>> ∃H ∈ C_Functions
>> ∀D ∈ x86_Machine_Code_of_C_Functions
>> such that H(D,D) = Halts(D,D)
>>
>> In both cases infinite sets are examined to see
>> if any H exists with the required properties.
> 
> That says nothing about correct simulation. It says
> something abuout some D but not whether it is correctly
> simulated. Also nothing is said about templates or
> infinite sets. At the end is claimed that some
> infinite sets are examined but not who examined, nor
> how, nor what was found in the alleged examination.
> 

*Formalizing the Linz Proof structure*
∃H  ∈ Turing_Machines
∀x  ∈ Turing_Machines_Descriptions
∀y  ∈ Finite_Strings
such that H(x,y) = Halts(x,x)

The above disavows Richard's claim based on a misinterpretation of
Linz that the Linz proof is about a single specific Turing machine.

    The domain of this problem is to be taken as the set of
    all Turing machines and all w; that is, we are looking
    for a single Turing machine that, given the description
    of an arbitrary M and w, will predict whether or not the
    computation of M applied to w will halt.

Linz <IS NOT> looking for a single machine that gets the wrong answer.
Linz is looking for at least one Turing Machine that gets the right
answer: ∃H ∈ Turing_Machines

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