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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 10:40:29 -0500
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On 5/16/2025 2:27 AM, Mikko wrote:
> On 2025-05-15 16:47:49 +0000, olcott said:
> 
>> On 5/15/2025 11:08 AM, 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.
>>
>> These things cannot be investigated in great
>> depth because there is no fully encoded UTM in
>> any standard language.
> 
> Investigations do not need a standard language. For an investigation an
> ad hoc language is good enough and usually better.
> 

Until I made this concrete people kept assuming that
an input DD could be defined that actually does the
opposite of whatever value that its simulating termination
analyzer HHH returns.

int main()
{
   DD(); // HHH cannot report on the behavior of its caller.
}

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