Re: DDD specifies recursive emulation to HHH and halting to HHH1

Am Fri, 28 Mar 2025 13:56:31 -0500 schrieb olcott:

On 3/27/2025 5:01 PM, joes wrote:

Am Thu, 27 Mar 2025 12:50:12 -0500 schrieb olcott:

On 3/27/2025 2:18 AM, Fred. Zwarts wrote:

Op 27.mrt.2025 om 04:09 schreef olcott:

On 3/26/2025 8:22 PM, Richard Damon wrote:

 

Non-Halting is that the machine won't reach its final staste even
if an unbounded number of steps are emulated. Since HHH doesn't do
that, it isn't showing non-halting.

DDD emulated by any HHH will never reach its final state in an
unbounded number of steps.
DDD emulated by HHH1 reaches its final state in a finite number of
steps.

It is not very interesting to know whether a simulator reports that
it is unable to reach the end of the simulation of a program that
halts in direct execution.

That IS NOT what HHH is reporting.

That is exactly what it does, and you have said so before(tm).

You are saying that HHH is reporting that HHH is screwing up THAT IS
FALSE. HHH IS REPORTING THAT DDD IS SCREWING UP.

How so? It mostly calls HHH.

HHH correctly rejects DDD because DDD correctly emulated by HHH cannot
possibly reach its own final halt state.

DDD doesn't *do* anything, it is being simulated. HHH can't reach DDD's
existing halt state.

DDD specifies a recursive emulation relationship with HHH

No, only when HHH simulates it.

It is interesting to know:
'Is there an algorithm that can determine for all possible inputs
whether the input specifies a program that [...]
halts when directly executed?'
This question seems undecidable for Olcott.

It is the halts while directly executed that is impossible for all
inputs. No TM can ever report on the behavior of the direct execution
of any other TM.

The direct execution of a TM is obviously computable from its
description.

It seems you disagreed.

A TM can only report on the behavior that the machine code of another
TM specifies. When it specifies a pathological relationship then the
behavior caused by the pathological relationship MUST BE REPORTED.

No, the machine code doesn't "specify a pathological relationship",
that is purely a feature of trying to simulate it with the included
simulator.

The classic HP counter-example input HAS ALWAYS SPECIFIED A PATHOLOGICAL
RELATIONSHIP TO ITS DECIDER.

Only when simulated.

The question has always been what Boolean value can H correctly return
when D is able to do the opposite of whatever value that H returns?

None.

When we prove that it is impossible for D to do the opposite of whatever
value that H returns the original question becomes moot.

How is it impossible? H by definition returns a boolean, and D halts or
enters an infinite loop based on that. Nothing magical.

--
Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.