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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 04:59:56 +0800
Organization: A noiseless patient Spider
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Message-ID: <d4b02c8deb6dd72c7bf143b07c2752d93b825b1d.camel@gmail.com>
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In-Reply-To: <102cp0e$26clp$1@dont-email.me>

On Wed, 2025-06-11 at 15:30 -0500, olcott wrote:
> On 6/11/2025 2:45 PM, wij wrote:
> > On Wed, 2025-06-11 at 14:39 -0500, olcott wrote:
> > > On 6/11/2025 2:31 PM, wij wrote:
> > > > 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 requi=
red by simulation.
> > > > > > >=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=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 s=
ee.
> > > >=20
> > > > On the contrary, what the HP proves is very useful.
> > > >=20
> > >=20
> > > I am not talking about the halting problem, I have always
> > > been talking about the conventional halting problem proof.
> > > THIS PROOF IS WRONG
> >=20
> > When talking about proof, we say it is valid or not. By doing so, we ha=
ve
> > to unambiguously pose the problem and the derivation to the conclusion.
> > The HP proof just did that.
> >=20
>=20
> It may seem that way if you pay less than 100%
> complete attention.
>=20
> The HP proof depends on an *INPUT* that does
> the opposite of whatever value that H returns
> and no such *INPUT* can possibly exist.

That is absolutely correct. No such *INPUT* (i.e. D) can possible exit is b=
ecause
the H inside D does not exist at all.
So, if the H is assumed to exist, then D will exist to make H undecidable.