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From: wij <wyniijj5@gmail.com>
Newsgroups: comp.theory
Subject: Re: How to write a self-referencial TM?
Date: Sun, 18 May 2025 03:26:44 +0800
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On Sat, 2025-05-17 at 15:45 +0100, Mike Terry wrote:
> 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 f=
unction (which calls
> > > > > > > > > > > > > > > > itself):
> > > > > > > > > > > > > > > >=20
> > > > > > > > > > > > > > > > void D() {
> > > > > > > > > > > > > > > > =C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=
=C2=A0 D();
> > > > > > > > > > > > > > > > }
> > > > > > > > > > > > > > > >=20
> > > > > > > > > > > > > > > > Easy?
> > > > > > > > > > > > > > > >=20
> > > > > > > > > > > > > > > >=20
> > > > > > > > > > > > > > >=20
> > > > > > > > > > > > > > > That is not a TM.
> > > > > > > > > > > > > >=20
> > > > > > > > > > > > > > It is a C program that exists. Therefore, there=
 must be a equivalent TM.
> > > > > > > > > > > > > >=20
> > > > > > > > > > > > > > > To make a TM that references itself the close=
st
> > > > > > > > > > > > > > > thing is a UTM that simulates its own TM sour=
ce-code.
> > > > > > > > > > > > > >=20
> > > > > > > > > > > > > > How does a UTM simulate its own TM source-code?
> > > > > > > > > > > > > >=20
> > > > > > > > > > > > >=20
> > > > > > > > > > > > > You run a UTM that has its own source-code on its=
 tape.
> > > > > > > > > > > >=20
> > > > > > > > > > > > What is exactly the source-code on its tape?
> > > > > > > > > > > >=20
> > > > > > > > > > >=20
> > > > > > > > > > > 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.
> > > > > > > > > > >=20
> > > > > > > > > > > So to answer your question, the "source-code on its t=
ape" is the result of
> > > > > > > > > > > applying
> > > > > > > > > > > the
> > > > > > > > > > > UTM's
> > > > > > > > > > > particular scheme to the combination (UTM, input tape=
) that is to be simulated.
> > > > > > > > > > >=20
> > > > > > > > > > > If you're looking for the exact string symbols, obvio=
usly you would need to
> > > > > > > > > > > specify
> > > > > > > > > > > the
> > > > > > > > > > > exact
> > > > > > > > > > > UTM
> > > > > > > > > > > being used, because every UTM will have a different a=
nswer to your question.
> > > > > > > > > > >=20
> > > > > > > > > > >=20
> > > > > > > > > > > Mike.
> > > > > > > > > >=20
> > > > > > > > > > People used to say UTM can simulate all TM. I was quest=
ing such a UTM.
> > > > > > > > > > Because you said "Every UTM ...", so what is the source=
 of such UTM?
> > > > > > > > >=20
> > > > > > > > > Yes, a UTM can simulate any TM including itself.=C2=A0 (N=
othing magical changes when a
> > > > > > > > > UTM
> > > > > > > > > simulates
> > > > > > > > > itself, as opposed to some other TM.)
> > > > > > > >=20
> > > > > > > > Supposed UTM exists, and denoted as U(X), X denotes the tap=
e 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.
> > > > > > >=20
> > > > > > > There is no self-reference trap.
> > > > > > >=20
> > > > > > > In your notation:
> > > > > > >=20
> > > > > > > -=C2=A0 f represents some computation.
> > > > > > > -=C2=A0 U(f) represents U being run with f on its tape.
> > > > > > > =C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 Note this is itself a co=
mputation, distinct from f of course
> > > > > > > =C2=A0=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 but having the same beha=
viour.
> > > > > > > -=C2=A0 U(U(f)) represents U simulating the previous computat=
ion.
> > > > > > >=20
> > > > > > > There is no reason U(f) cannot be simulated by U.=C2=A0 U wil=
l have no knowledge that it is
> > > > > > > "simulating
> > > > > > > itself", and will just simulate what it is given.
> > > > > > >=20
> > > > > > >=20
> > > > > > > Mike.
> > > > > >=20
> > > > > > Sorry for not being clear on the UTM issue (I wanted to mean se=
veral things in one post).
> > > > > > You are right there is no self-reference.
> > > > > > I mean 'UTM' is not a complete, qualified TM because the conten=
ts of the tape
> > > > > > would not be defined. Saying "UTM can simulate any TM" is misle=
ading because
> > > > > > no such TM (UTM as TM) exists.
> > > > >=20
> > > > > What do you mean "the contents of the tape would not be defined"?=
=C2=A0 A TM is /equipped/ with
> > > > > an
> > > > > infinite tape, but the /contents/ of that tape are not a part of =
that TM's definition.
> > > > >=20
> > > > > For example we could build a TM P that decides whether a number i=
s prime.=C2=A0 Given a number n,
> > > > > we
> > > > > convert n into the input tape representation of n, and run P with=
 that tape as input.
> > > > >=20
> > > > > It's essentially no different for UTMs.=C2=A0 Such a UTM certainl=
y is a "complete TM", equipped
> > > > > with
> > > > > its
> > > > > own input tape.=C2=A0 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!=C2=A0 [Similarly we don=
't know what's on P's input
> > > > > tape,
> > > > > until
> > > > > we know what n we want it to test for primeness.]=C2=A0 Once you =
say what computation you want
> > > > > the
> > > > > UTM to
> > > > > simulate we can build a tape string to perform that particular si=
mulation.=C2=A0 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.
> > > > >=20
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