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From: joes <noreply@example.com>
Newsgroups: comp.theory
Subject: Re: D correctly simulated by H cannot possibly halt --- templates and
 infinite sets
Date: Thu, 30 May 2024 09:11:40 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
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Am Wed, 29 May 2024 22:48:45 -0500 schrieb olcott:
> On 5/29/2024 9:55 PM, Richard Damon wrote:
>> On 5/29/24 10:36 PM, olcott wrote:
>>> On 5/29/2024 9:25 PM, Richard Damon wrote:
>>>> On 5/29/24 9:55 PM, olcott wrote:
>>>>> When the category is examined all at once then there is no need
>>>>> to look at each individual element.
>>>> So, which one or ones gave the correct answer for their input?

>>> *Formalizing the Linz Proof structure*
>>> ∃H  ∈ Turing_Machines
>>> ∀x  ∈ *Turing_Machines_Descriptions*
>>> ∀y  ∈ Finite_Strings
>>> such that H(x,y) = Halts(x,y)
>>>
>>> When we formalize it that way then some simulating halt deciders
>>> get the correct answer.
>>>
>>> *Everyone else implicitly assumes this incorrect formalization*
>>> ∃H  ∈ Turing_Machines
>>> ∀x  ∈ *Turing_Machines*
>>> ∀y  ∈ Finite_Strings
>>> such that H(x,y) = Halts(x,y)
>>>
>> Nope.
>> You just don't understand the meaning of a "Description" in the problem.
>> 
> I have an OCD/Aspergers degree of single-minded focus.
Checks out.

> *A deciders compute the mapping*
> FROM ITS INPUTS
> *to it own accept or reject state*
> 
> *Deciders cannot take*
> ACTUAL TURING MACHINES AS INPUTS
> 
> *Deciders can only take*
> FINITE STRINGS AS INPUTS
Poetic.
What is an „actual Turing machine”?

-- 
joes