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From: wij <wyniijj5@gmail.com>
Newsgroups: comp.theory
Subject: Re: Simulation vs. Execution in the Halting Problem
Date: Thu, 12 Jun 2025 03:31:58 +0800
Organization: A noiseless patient Spider
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In-Reply-To: <102ckje$25dg0$2@dont-email.me>

On Wed, 2025-06-11 at 14:14 -0500, olcott wrote:
> On 6/11/2025 1:25 PM, wij wrote:
> > On Wed, 2025-06-11 at 12:59 -0500, olcott wrote:
> > > > >=20
> > > > > Yes all other people (especially Dennis Bush) are saying
> > > > > that H(D) is required to report on the behavior of the
> > > > > direct execution of D() never noticing that this stupidly
> > > > > requires H(D) to report on the behavior of its caller.
> > > >=20
> > > > If the H above means the H that the HP refers to. The H is required=
 to
> > > > report its argument's behavior (ie. by H(D)). But NOT required by s=
imulation.
> > >=20
> > > It turns out that no one ever noticed that simulating halt
> > > deciders nullify the HP counter-example input in that this
> > > input cannot possibly reach its contradictory part.
> > >=20
> > > > The HP does not care what D does (simply to say).
> > > >=20
> > >=20
> > > Everyone says that H(D) must re[port on the behavior of
> > > the direct execution of D().
> >=20
> > That is what the HP asks.
> >=20
> > > > The HP only requires: H(D)=3D=3D1 iff D() halts
> > > >=20
> > > >=20
> > >=20
> > > int main()
> > > {
> > > =C2=A0=C2=A0=C2=A0 D(); // calls H(D)
> > > }
> > >=20
> > > Which requires H(D) to report on the behavior of its
> > > caller instead of reporting on the behavior that its
> > > input actually specifies.
> >=20
> > That is no problem. H does not care what D does inside (simply to say).
> > The HP simply asks for a H that "H(D)=3D=3D1 iff D() halts".
> >=20
>=20
> Which requires H to report on something that it cannot possibly see.

On the contrary, what the HP proves is very useful.