Path: news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail
From: Mike Terry <news.dead.person.stones@darjeeling.plus.com>
Newsgroups: comp.theory
Subject: Re: How to write a self-referencial TM?
Date: Sat, 17 May 2025 15:45:24 +0100
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On 17/05/2025 04:01, wij wrote:
> On Fri, 2025-05-16 at 23:51 +0100, Mike Terry wrote:
>> On 16/05/2025 20:35, wij wrote:
>>> On Fri, 2025-05-16 at 16:33 +0100, Mike Terry wrote:
>>>> On 16/05/2025 12:40, wij wrote:
>>>>> On Fri, 2025-05-16 at 03:26 +0100, Mike Terry wrote:
>>>>>> On 16/05/2025 02:47, wij wrote:
>>>>>>> On Fri, 2025-05-16 at 01:40 +0100, Mike Terry wrote:
>>>>>>>> On 15/05/2025 19:49, 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?
>>>>>>>>
>>>>>>>> Yes, a UTM can simulate any TM including itself.  (Nothing magical changes when a UTM
>>>>>>>> simulates
>>>>>>>> itself, as opposed to some other TM.)
>>>>>>>
>>>>>>> Supposed UTM exists, and denoted as U(X), X denotes the tape contents of the
>>>>>>> encoding of a TM. And, U(X) should function the same like X.
>>>>>>> Given instance U(U(f)), it should function like f from the above definition.
>>>>>>> But, U(U(f)) would fall into a 'self-reference' trap.
>>>>>>
>>>>>> There is no self-reference trap.
>>>>>>
>>>>>> In your notation:
>>>>>>
>>>>>> -  f represents some computation.
>>>>>> -  U(f) represents U being run with f on its tape.
>>>>>>        Note this is itself a computation, distinct from f of course
>>>>>>        but having the same behaviour.
>>>>>> -  U(U(f)) represents U simulating the previous computation.
>>>>>>
>>>>>> There is no reason U(f) cannot be simulated by U.  U will have no knowledge that it is
>>>>>> "simulating
>>>>>> itself", and will just simulate what it is given.
>>>>>>
>>>>>>
>>>>>> Mike.
>>>>>
>>>>> Sorry for not being clear on the UTM issue (I wanted to mean several things in one post).
>>>>> You are right there is no self-reference.
>>>>> I mean 'UTM' is not a complete, qualified TM because the contents of the tape
>>>>> would not be defined. Saying "UTM can simulate any TM" is misleading because
>>>>> no such TM (UTM as TM) exists.
>>>>
>>>> What do you mean "the contents of the tape would not be defined"?  A TM is /equipped/ with an
>>>> infinite tape, but the /contents/ of that tape are not a part of that TM's definition.
>>>>
>>>> For example we could build a TM P that decides whether a number is prime.  Given a number n, we
>>>> convert n into the input tape representation of n, and run P with that tape as input.
>>>>
>>>> It's essentially no different for UTMs.  Such a UTM certainly is a "complete TM", equipped with
>>>> its
>>>> own input tape.  Of course we don't know what's on the input tape because nobody has said yet
>>>> what
>>>> computation we are asking it to simulate!  [Similarly we don't know what's on P's input tape,
>>>> until
>>>> we know what n we want it to test for primeness.]  Once you say what computation you want the
>>>> UTM to
>>>> simulate we can build a tape string to perform that particular simulation.  That is the case
>>>> /whatever/ computation we come up with, so it is simply the case [not misleading] that the UTM
>>>> can
>>>> simulate any computation.
>>>>
>>>>
>>>> Mike.
>>>
>>> TM has no I/O mechanism. 'Computation' always means the contents of the tape
>>> is defined (fixed before run).
>>>
>>
>> Correct, and correct.
>>
>> So... What do you mean "the contents of the tape would not be defined"?
>>
>>
>> Mike.
> 
> In "UTM simulates itself", denoted as U(U(f)), the f would not be defined.

Eh?  The f was something /you/ introduced!  You said it represents some computation which UTM U 
simulates.  How can f suddenly become undefined after you defined it?

Do you mean that f would not be on the input tape for (outer)U?  That's not the case at all.  In 
U(f), the input tape for U contains a representation of f.  When (outer)U simulates (inner)U 
simulating f, (outer)U's tape contains a representation of computation U(f), which internally 
contains the original representation of f.  The f is still there and equally well defined in U(U(f)).

I think you would benefit from being more explicit and generally more careful in your notation!

Using notation <P,I> to mean U's input tape representation of "TM P, running with input I":

    Your U(f)      is U(<fp,fi>)		// fp = TM(f), fi=InputTape(f)
    Your U(U(f))   is U((<U,<fp,fi>>)

f is still there!  It has not become "undefined".

You gloss over the details and become confused - just think it through step by step.


Mike.