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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: How to write a self-referencial TM?
Date: Fri, 16 May 2025 10:47:34 -0500
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On 5/16/2025 2:45 AM, Mikko wrote:
> On 2025-05-15 20:08:54 +0000, wij said:
> 
>> On Thu, 2025-05-15 at 14:15 -0500, olcott wrote:
>>> On 5/15/2025 1:49 PM, wij wrote:
>>>> On Thu, 2025-05-15 at 17:08 +0100, Mike Terry wrote:
>>>>> On 14/05/2025 18:53, wij wrote:
>>>>>> On Wed, 2025-05-14 at 12:24 -0500, olcott wrote:
>>>>>>> On 5/14/2025 11:43 AM, wij wrote:
>>>>>>>> On Wed, 2025-05-14 at 09:51 -0500, olcott wrote:
>>>>>>>>> On 5/14/2025 12:13 AM, wij wrote:
>>>>>>>>>> Q: Write a turing machine that performs D function (which 
>>>>>>>>>> calls itself):
>>>>>>>>>>
>>>>>>>>>> void D() {
>>>>>>>>>>      D();
>>>>>>>>>> }
>>>>>>>>>>
>>>>>>>>>> Easy?
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> That is not a TM.
>>>>>>>>
>>>>>>>> It is a C program that exists. Therefore, there must be a 
>>>>>>>> equivalent TM.
>>>>>>>>
>>>>>>>>> To make a TM that references itself the closest
>>>>>>>>> thing is a UTM that simulates its own TM source-code.
>>>>>>>>
>>>>>>>> How does a UTM simulate its own TM source-code?
>>>>>>>>
>>>>>>>
>>>>>>> You run a UTM that has its own source-code on its tape.
>>>>>>
>>>>>> What is exactly the source-code on its tape?
>>>>>>
>>>>>
>>>>> Every UTM has some scheme which can be applied to a (TM & input 
>>>>> tape) that is to be simulated.
>>>>> The
>>>>> scheme says how to turn the (TM + input tape) into a string of 
>>>>> symbols that represent that
>>>>> computation.
>>>>>
>>>>> So to answer your question, the "source-code on its tape" is the 
>>>>> result of applying the UTM's
>>>>> particular scheme to the combination (UTM, input tape) that is to 
>>>>> be simulated.
>>>>>
>>>>> If you're looking for the exact string symbols, obviously you would 
>>>>> need to specify the exact
>>>>> UTM
>>>>> being used, because every UTM will have a different answer to your 
>>>>> question.
>>>>>
>>>>>
>>>>> Mike.
>>>>
>>>> People used to say UTM can simulate all TM. I was questing such a UTM.
>>>> Because you said "Every UTM ...", so what is the source of such UTM?
>>>>
>>>>
>>>
>>> The TM description language is more accurately
>>> referred to as the TM specification language.
>>>
>>> A UTM is a hypothetical thing that is specified
>>> to have some source source-code that it operates
>>> on yet none of the details of this are ever
>>> fully elaborated.
>>>
>>> That is why I needed to use the x86 language
>>> as a fully specified proxy. With my x86utm
>>> operating system we make a 100% concrete
>>> simulating termination analyzer such that
>>> zero of the details are "abstracted away".
>>>
>>> It is the details that have been "abstracted away"
>>> by the abstractions that cause the conventional
>>> halting problem proofs to be insufficiently
>>> understood.
>>
>> Unfortunely, refuting HP suggests halting decider is a real thing.
>> Proving by "abstracted away" the real part?
> 
> In which way can a proof that a halting decider does not exist
> suggest that a halting decider is a real thing?
> 
> The concept of halting decider is a real concept in the same sense
> as Arsitotle's concept of unicorn is a real concept but does that
> mean that a unicorn and a halting decider are real things?
> 

I have only refuted the standard proof.
A halt decider HHH having a domain of DD and DDD
correctly maps its inputs to the actual behavior
that they actually specify.


-- 
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer