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From: wij <wyniijj5@gmail.com>
Newsgroups: comp.theory
Subject: Re: What it would take...
Date: Sat, 10 May 2025 23:35:56 +0800
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On Sat, 2025-05-10 at 10:07 -0500, olcott wrote:
> On 5/9/2025 9:18 PM, Richard Damon wrote:
> > On 5/9/25 9:11 PM, Richard Heathfield wrote:
> > > The HHH code doesn't exactly invite confidence in its author, and his=
=20
> > > theory is all over the place, but a thought experiment suggests itsel=
f.
> > >=20
> > > If we were not all wasting our time bickering with a career=20
> > > bickerer... if we were to really /really/ try, could we patch up his=
=20
> > > case and send him on to his Turing Award? And if so, how?
> > >=20
> > > ISTR that there is suspected to be a theoretical window for him, so I=
=20
> > > suppose what I'm asking is what sort of boathook we would need to pok=
e=20
> > > that window a little wider.
> > >=20
> > > Can he even get there from here? Evidence would suggest that=20
> > > simulation is a dead end unless he can find a way to get the simulate=
d=20
> > > program to include its own simulation in its behaviour, which he has=
=20
> > > not yet managed to do - but /is/ there a way?
> > >=20
> > > Or could he abandon simulation completely and instead write a TM=20
> > > parser that builds an AST and walks it looking for evidence of=20
> > > terminating or looping? If he could, would that turn the trick?
> > >=20
> > > Or do we have a latter day Cantor waiting in the wings to close the=
=20
> > > window once and for all?
> > >=20
> > > Is there, in short, any way of putting out this un-halting flame war=
=20
> > > and turning this group to better use?
> > >=20
> >=20
> > If he was willing to include the code for HHH in the input representing=
=20
> > DDD, then HHH would be able to atempt to correctly emulate this input.
> >=20
>=20
> DDD and HHH have always been in the same memory space.
> DDD is the program under test and HHH is the test program.
>=20
> > There have been methods put forward, that given an acceptace of the=20
> > detectability of DDD calling HHH, which can only be done it seems if we=
=20
> > make the system non-turing complete by saying that the input program an=
d=20
> > the decider are put into the same memory space, and we are not allowed=
=20
> > to "copy" an algorithm to make a new copy, but only call the origianal=
=20
> > version so HHH can detect the recursion by reference to that address=
=20
> > that some versions of programs that do this "recursive simulation" can=
=20
> > be correctly decider (but not all, like the pathological version).
> >=20
>=20
> HHH is essentially a UTM thus EVERYTHING is in the memory space
> of its UTM tape.
>=20
> > In this method, the Decider detecting the recursion, tries emulating th=
e=20
> > code in two parrallel branches based on both possible answers, and if=
=20
> > one branch matches the behavior of the answer, it can return that answ3=
er.
> >=20
>=20
> We can emulate a branch as if a conditional expression
> was true and as if it was false. HHH determines the
> behavior of DDD on the basis of what would happen if
> HHH never aborted.
>=20
> <MIT Professor Sipser agreed to ONLY these verbatim words 10/13/2022>
> =C2=A0=C2=A0=C2=A0=C2=A0 If simulating halt decider H correctly simulates=
 its
> =C2=A0=C2=A0=C2=A0=C2=A0 input D until H correctly determines that its si=
mulated D
> =C2=A0=C2=A0=C2=A0=C2=A0 *would never stop running unless aborted* then
>=20
> > Thus, inputs like DDD() that always halt on the return of HHH(DDD) will=
=20
> > be correctly determined to be halting, and a varient that just goes int=
o=20
> > an infinite loop can be such detected by well know procedures as non-=
=20
> > halting.
> >=20
>=20
> When HHH continues to emulate DDD until HHH sees the
> repeating pattern that would prevent DDD from ever
> terminating
>=20
> =C2=A0=C2=A0=C2=A0=C2=A0 H can abort its simulation of D and correctly re=
port that D
> =C2=A0=C2=A0=C2=A0=C2=A0 specifies a non-halting sequence of configuratio=
ns.
> </MIT Professor Sipser agreed to ONLY these verbatim words 10/13/2022>
>=20
> > The pathological DD() is detected as pathological, and we can perhaps=
=20
> > extend the definition to allow it to respiond with an "I give up, I=20
> > don't know the answer" response, but such an extention explicitly does=
=20
> > NOT meet the requirements, but is better than not answering or giving a=
=20
> > wrong answer.
> >=20
> > The problem is this result doesn't meet Peter's Goal, as it isn't reall=
y=20
> > the Halting Problem that he has his major problem with, but the fact=
=20
> > that Turings Proof became the basis for a number of broader proofs of=
=20
> > incompleteness and undeciability that fills formal logic.
> >=20
> > This is what he can't handle, and this is because he just doesn't reall=
y=20
> > understand how all of the works because his mental models of logic is=
=20
> > just way to small and simple.
>=20
> Dodge and weave is all you know.
>=20
> int DD()
> {
> =C2=A0=C2=A0 int Halt_Status =3D HHH(DD);
> =C2=A0=C2=A0 if (Halt_Status)
> =C2=A0=C2=A0=C2=A0=C2=A0 HERE: goto HERE;
> =C2=A0=C2=A0 return Halt_Status;
> }
>=20
> It is a verified fact that DD correctly emulated
> by any simulating termination analyzer HHH specifies
> a non-terminating sequence of configurations.
>=20

Nope.=20
POOH is intended to decide whether the input D is "impossible" input or not=
..