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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: How to write a self-referencial TM?
Date: Tue, 20 May 2025 23:41:44 -0500
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On 5/19/2025 5:39 AM, Mikko wrote:
> On 2025-05-16 15:40:29 +0000, olcott said:
> 
>> 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.
> 
> That need not and should not be assumed. That can be constructively
> proven.
> 
> Which doesn't matter to any investigation.
> 

There are only two ways to try to define a DD
that actually does the opposition of whatever
value that is termination analyzer returns.
Neither of the work.

int main()
{
   DDD() // HHH called from DDD can know nothing of it caller.
}

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