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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 10:43:02 -0500
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In-Reply-To: <1006pnk$3lfep$1@dont-email.me>

On 5/16/2025 2:33 AM, Mikko wrote:
> On 2025-05-15 20:50:34 +0000, olcott said:
> 
>> On 5/15/2025 2:57 PM, wij wrote:
>>> On Thu, 2025-05-15 at 11:47 -0500, olcott wrote:
>>>> 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.
>>>
>>> Sort of.
>>>
>>>> If there was such a UTM then examining things
>>>> like a termination analyzer would be too difficult
>>>> because of the volume of details. Even moving a
>>>> single value to a specific memory location can
>>>> take many many steps.
>>>
>>> So, which part of POOH is "fully encoded UTM"
>>>
>>>> A RASP machine
>>>> https://en.wikipedia.org/wiki/Random-access_stored-program_machine
>>>> is a much better fit for examining the details of any
>>>> complex algorithm.
>>>>
>>>> The x86 language is essentially the same thing as a RASP
>>>> machine for all computations that can be accomplished
>>>> with the amount of memory that is available.
>>>
>>> Absolutely false. POOH is the example that rejected TM/RASP instead 
>>> of C.
>>>
>>> In trying making P!=NP proof (may have defects, I just leave it there 
>>> to improve)
>>> https://sourceforge.net/projects/cscall/files/MisFiles/PNP-proof- 
>>> en.txt/download
>>> I feel TM would be very long and tedious, so I claimed that no 
>>> *algorithm* can
>>> solve NPC (algorithmic) problems. (thanks to olcott, this proof was 
>>> inspired in
>>> refuting POOH.)
>>>
>>> See also Spu in my recent post. TM is very low-level to solve many 
>>> idea of problems.
>>>
>>>> To be a computable function within a model of computation
>>>> a sequence of the steps of a specific algorithm must be
>>>> applied to (an often finite string) input to derive an output.
>>>> https://en.wikipedia.org/wiki/Computable_function
>>>>
>>>> When computing the sum() function the steps of the algorithm
>>>> of arithmetic must be applied to the inputs.
>>>>
>>>> *When computing the halt() function steps with a simulating*
>>>> *termination analyzer the behavioral steps specified by the*
>>>> *input must be simulated according to the computer language*
>>>> *of this input*
>>>>
>>>> *I may be wrong yet it seems to me that*
>>>> Computer science never knew these things before in that
>>>> it never placed any limit on the type of algorithm that
>>>> must be performed.
>>>>
>>>> I think that it was Ben that said that one of two
>>>> functions that do nothing besides return true or false
>>>> is correct on all of the counter-example inputs
>>>> to the halting problem.
>>>>
>>>> When we require that a mapping be computed from an
>>>> input, then this idea is rejected.
>>>>
>>>
>>> You are excellent in quoting tautology to support your claims.
>>>
>>
>> Most people don't know that a mapping must be
>> computed from the inputs, hence Ben's mistake.
> 
> Most people don't even know what mappings are. Most people don't
> make mistakes just because they don't know what mappings are.
> 
> Ben does not make mistakes just because most people don't know
> something that Ben does know.
> 

Ben was wrong when he said that there are a
pair of computable functions such that one
of them always gets the correct halt status
decision. IGNORING THE INPUTS IT NOT ALLOWED

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