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Re: HHH(DD) Input exactly matches non-halting behavior

From Kaz Kylheku <643-408-1753@kylheku.com>
Newsgroups comp.theory
Subject Re: HHH(DD) Input exactly matches non-halting behavior
Date 2025-10-20 22:57 +0000
Organization A noiseless patient Spider
Message-ID <20251020154719.424@kylheku.com> (permalink)
References (6 earlier) <10d61t7$3east$1@dont-email.me> <20251020133542.246@kylheku.com> <10d6894$3g67m$1@dont-email.me> <20251020140856.203@kylheku.com> <10d6agc$3gokt$1@dont-email.me>

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On 2025-10-20, olcott <polcott333@gmail.com> wrote:
> On 10/20/2025 4:11 PM, Kaz Kylheku wrote:
>> On 2025-10-20, olcott <polcott333@gmail.com> wrote:
>>> On 10/20/2025 3:47 PM, Kaz Kylheku wrote:
>>>>> Simulating Termination Analyzer HHH correctly simulates its input until:
>>>>>
>>>>> (a) It correctly detects that its simulated input cannot
>>>>>        possibly reach its own simulated final halt state then:
>>>>>        abort simulation and return 0 rejecting its input as non-halting.
>>>>>
>>>>> (b) Simulated input reaches its simulated "return" statement: return 1.
>>>>
>>>> You are missing two more cases:
>>>>
>>>>    (c) It incorrectly detects that its simulated input
>>>>        is non-terminating, and wrongly rejects it with 0 as non-halting.
>>>>
>>>
>
><Input to LLM systems>
>
> Trace through the simulation step-by-step to see of (a) (b) or (c) is 
> matched before doing anything else.

It's not that (a) isn't matched, it's that it's not correct. 

Yes, there is a condition that is checked for about an execution
trace event hitting the DD address several times, without a return
being seen from the HHH(DD) call.

Those hits are not in the same simulation, and so do not constitute a
control flow loop!

It is not correct; DD halts.

DD halts because of HHH(DD) == 0; it is inescapable.

It's not your fault that it's wrong, because no matter how clever you
make the test, it will turn out wrong for the decider's own tailor-made
diagonal case.

> (a) It correctly detects that its simulated input cannot
>      possibly reach its own simulated final halt state then:

That's not what it's deciding though. It's substituting a concrete
set of conditions, and you /believe/ that those conditions indicate
that the simulated input doesn't terminate.

What the conditions test is not in question; what is in question is
your claim that the conditions indicate the target's non-termination;
they don't.

It can be precisely articulated why they don't.

A "free running" tower of simulations constantly launches new
simulations with spontaneously begin at the address DD. In a free
running tower, HHH(DD) does not return. So it is correct to observe
that it is non-terminating behavior.

In an "aborted" tower of simulations, there is the same launching of
new simulations which spontaneously begin at the address DD.
///For some initial period/// this behavior continues; until HHH
decides "enough!" and returns 0.

In every simuation levrel, HHH(DD) is working toward that: allowing a
few new simulations of DD to start (so execution events at address DD
are spontaneously observed) but then to pull the plug and return.

Your top-level HHH(DD) call only caries its simulation level far
just far enough not to see that the next simulated HHH(DD) returns 0
exactly as it does.

It wrongly concludes after something like two observations of the
instruction pointer hitting DD that there is a control flow
loop/recursion that will repeat forever.

Almost nothing repeats forever in the aborting simulation in which every
simulation level is run by the aborting HHH.

Except for one thing: the launching of new simulation nestings
(all of which terminate!)

-- 
TXR Programming Language: http://nongnu.org/txr
Cygnal: Cygwin Native Application Library: http://kylheku.com/cygnal
Mastodon: @Kazinator@mstdn.ca

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My two specifications are equivalent HHH(DD)==0 is correct olcott <polcott333@gmail.com> - 2025-10-18 06:20 -0500
  Re: My two specifications are equivalent HHH(DD)==0 is correct Richard Damon <Richard@Damon-Family.org> - 2025-10-18 07:49 -0400
  Re: My two specifications are equivalent HHH(DD)==0 is correct vallor <vallor@vallor.earth> - 2025-10-18 14:43 +0000
    Re: My two specifications are equivalent HHH(DD)==0 is correct olcott <polcott333@gmail.com> - 2025-10-18 09:48 -0500
      Re: My two specifications are equivalent HHH(DD)==0 is correct vallor <vallor@vallor.earth> - 2025-10-18 15:53 +0000
        Re: My two specifications are equivalent HHH(DD)==0 is correct olcott <polcott333@gmail.com> - 2025-10-18 10:59 -0500
          Re: My two specifications are equivalent HHH(DD)==0 is correct Kaz Kylheku <643-408-1753@kylheku.com> - 2025-10-18 17:06 +0000
            Re: My two specifications are equivalent HHH(DD)==0 is correct olcott <polcott333@gmail.com> - 2025-10-18 12:09 -0500
              Re: My two specifications are equivalent HHH(DD)==0 is correct Kaz Kylheku <643-408-1753@kylheku.com> - 2025-10-18 20:16 +0000
                Re: My two specifications are equivalent HHH(DD)==0 is correct olcott <polcott333@gmail.com> - 2025-10-18 17:38 -0500
                Re: My two specifications are equivalent HHH(DD)==0 is correct Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-10-20 12:17 +0100
                Re: My two specifications are equivalent HHH(DD)==0 is correct olcott <polcott333@gmail.com> - 2025-10-20 12:08 -0500
                Re: My two specifications are equivalent HHH(DD)==0 is correct Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-10-21 09:02 +0100
                The halting problem is either incoherent or the proof wrong olcott <polcott333@gmail.com> - 2025-10-18 19:06 -0500
            Re: My two specifications are equivalent HHH(DD)==0 is correct olcott <polcott333@gmail.com> - 2025-10-18 17:26 -0500
              Re: My two specifications are equivalent HHH(DD)==0 is correct joes <noreply@example.org> - 2025-10-18 23:30 +0000
                Re: My two specifications are equivalent HHH(DD)==0 is correct olcott <polcott333@gmail.com> - 2025-10-18 20:06 -0500
                Re: My two specifications are equivalent HHH(DD)==0 is correct Kaz Kylheku <643-408-1753@kylheku.com> - 2025-10-19 18:12 +0000
                Re: My two specifications are equivalent HHH(DD)==0 is correct olcott <polcott333@gmail.com> - 2025-10-20 10:17 -0500
                Re: My two specifications are equivalent HHH(DD)==0 is correct Kaz Kylheku <643-408-1753@kylheku.com> - 2025-10-20 18:50 +0000
                Re: My two specifications are equivalent HHH(DD)==0 is correct olcott <polcott333@gmail.com> - 2025-10-20 14:50 -0500
                Re: My two specifications are equivalent HHH(DD)==0 is correct joes <noreply@example.org> - 2025-10-20 20:19 +0000
                Re: My two specifications are equivalent HHH(DD)==0 is correct olcott <polcott333@gmail.com> - 2025-10-20 15:24 -0500
                Re: My two specifications are equivalent HHH(DD)==0 is correct Kaz Kylheku <643-408-1753@kylheku.com> - 2025-10-20 20:54 +0000
                Re: My two specifications are equivalent HHH(DD)==0 is correct "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-10-20 14:50 -0700
                Re: My two specifications are equivalent HHH(DD)==0 is correct Kaz Kylheku <643-408-1753@kylheku.com> - 2025-10-20 20:35 +0000
                Re: My two specifications are equivalent HHH(DD)==0 is correct Kaz Kylheku <643-408-1753@kylheku.com> - 2025-10-20 20:33 +0000
                Re: My two specifications are equivalent HHH(DD)==0 is correct dbush <dbush.mobile@gmail.com> - 2025-10-20 16:57 -0400
                Re: My two specifications are equivalent HHH(DD)==0 is correct olcott <polcott333@gmail.com> - 2025-10-20 16:10 -0500
                Re: My two specifications are equivalent HHH(DD)==0 is correct dbush <dbush.mobile@gmail.com> - 2025-10-20 17:34 -0400
                Re: My two specifications are equivalent HHH(DD)==0 is correct Richard Heathfield <rjh@cpax.org.uk> - 2025-10-19 05:57 +0100
                Re: My two specifications are equivalent HHH(DD)==0 is correct olcott <polcott333@gmail.com> - 2025-10-19 09:40 -0500
                Re: My two specifications are equivalent HHH(DD)==0 is correct Kaz Kylheku <643-408-1753@kylheku.com> - 2025-10-19 18:24 +0000
                Re: My two specifications are equivalent HHH(DD)==0 is correct olcott <polcott333@gmail.com> - 2025-10-20 10:17 -0500
              Re: My two specifications are equivalent HHH(DD)==0 is correct Kaz Kylheku <643-408-1753@kylheku.com> - 2025-10-19 18:04 +0000
                Re: My two specifications are equivalent HHH(DD)==0 is correct Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2025-10-20 02:30 +0100
                Re: My two specifications are equivalent HHH(DD)==0 is correct olcott <polcott333@gmail.com> - 2025-10-20 10:54 -0500
                Re: My two specifications are equivalent HHH(DD)==0 is correct Kaz Kylheku <643-408-1753@kylheku.com> - 2025-10-20 18:31 +0000
                Re: My two specifications are equivalent HHH(DD)==0 is correct olcott <polcott333@gmail.com> - 2025-10-20 15:35 -0500
                Re: My two specifications are equivalent HHH(DD)==0 is correct Kaz Kylheku <643-408-1753@kylheku.com> - 2025-10-20 20:57 +0000
                Re: My two specifications are equivalent HHH(DD)==0 is correct olcott <polcott333@gmail.com> - 2025-10-20 10:15 -0500
                Re: My two specifications are equivalent HHH(DD)==0 is correct Kaz Kylheku <643-408-1753@kylheku.com> - 2025-10-20 18:35 +0000
                Re: My two specifications are equivalent HHH(DD)==0 is correct olcott <polcott333@gmail.com> - 2025-10-20 15:36 -0500
                Re: My two specifications are equivalent HHH(DD)==0 is correct Kaz Kylheku <643-408-1753@kylheku.com> - 2025-10-20 20:58 +0000
          Re: My two specifications are equivalent HHH(DD)==0 is correct "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-10-18 13:31 -0700
        Re: My two specifications are equivalent HHH(DD)==0 is correct Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-10-19 10:58 +0100
          Re: My two specifications are equivalent HHH(DD)==0 is correct olcott <polcott333@gmail.com> - 2025-10-19 09:57 -0500
          Re: My two specifications are equivalent HHH(DD)==0 is correct Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2025-10-19 12:56 -0700
            Re: My two specifications are equivalent HHH(DD)==0 is correct Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-10-20 11:50 +0100
      Re: My two specifications are equivalent HHH(DD)==0 is correct Kaz Kylheku <643-408-1753@kylheku.com> - 2025-10-18 17:03 +0000
        Re: My two specifications are equivalent HHH(DD)==0 is correct olcott <polcott333@gmail.com> - 2025-10-18 12:07 -0500
      Re: My two specifications are equivalent HHH(DD)==0 is correct "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-10-18 12:54 -0700
  Re: My two specifications are equivalent HHH(DD)==0 is correct "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-10-18 13:26 -0700
  Re: My two specifications are equivalent HHH(DD)==0 is correct Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-10-19 10:43 +0100
    Re: My two specifications are equivalent HHH(DD)==0 is correct olcott <polcott333@gmail.com> - 2025-10-19 09:55 -0500
      Re: My two specifications are equivalent HHH(DD)==0 is correct dbush <dbush.mobile@gmail.com> - 2025-10-19 12:15 -0400
      Re: My two specifications are equivalent HHH(DD)==0 is correct joes <noreply@example.org> - 2025-10-20 09:36 +0000
        Re: My two specifications are equivalent HHH(DD)==0 is correct olcott <polcott333@gmail.com> - 2025-10-20 10:59 -0500
          Re: My two specifications are equivalent HHH(DD)==0 is correct joes <noreply@example.org> - 2025-10-20 17:15 +0000
            Re: My two specifications are equivalent HHH(DD)==0 is correct olcott <polcott333@gmail.com> - 2025-10-20 12:33 -0500
          Re: My two specifications are equivalent HHH(DD)==0 is correct Kaz Kylheku <643-408-1753@kylheku.com> - 2025-10-20 19:03 +0000
            HHH(DD) Input exactly matches non-halting behavior olcott <polcott333@gmail.com> - 2025-10-20 14:17 -0500
              Re: HHH(DD) Input exactly matches non-halting behavior Kaz Kylheku <643-408-1753@kylheku.com> - 2025-10-20 20:47 +0000
                Re: HHH(DD) Input exactly matches non-halting behavior olcott <polcott333@gmail.com> - 2025-10-20 16:06 -0500
                Re: HHH(DD) Input exactly matches non-halting behavior Kaz Kylheku <643-408-1753@kylheku.com> - 2025-10-20 21:11 +0000
                Re: HHH(DD) Input exactly matches non-halting behavior olcott <polcott333@gmail.com> - 2025-10-20 16:44 -0500
                Re: HHH(DD) Input exactly matches non-halting behavior Kaz Kylheku <643-408-1753@kylheku.com> - 2025-10-20 22:57 +0000
                Re: HHH(DD) Input exactly matches non-halting behavior olcott <polcott333@gmail.com> - 2025-10-20 18:19 -0500
                Re: HHH(DD) Input exactly matches non-halting behavior dbush <dbush.mobile@gmail.com> - 2025-10-20 19:46 -0400
                Re: HHH(DD) Input exactly matches non-halting behavior Kaz Kylheku <643-408-1753@kylheku.com> - 2025-10-21 00:03 +0000
                Re: HHH(DD) Input exactly matches non-halting behavior olcott <polcott333@gmail.com> - 2025-10-20 19:14 -0500
                Re: HHH(DD) Input exactly matches non-halting behavior Kaz Kylheku <643-408-1753@kylheku.com> - 2025-10-21 01:29 +0000
                Re: HHH(DD) Input exactly matches non-halting behavior olcott <polcott333@gmail.com> - 2025-10-20 20:35 -0500
                Re: HHH(DD) Input exactly matches non-halting behavior Kaz Kylheku <643-408-1753@kylheku.com> - 2025-10-21 02:03 +0000
                Re: HHH(DD) Input exactly matches non-halting behavior olcott <polcott333@gmail.com> - 2025-10-20 21:22 -0500
                Re: HHH(DD) Input exactly matches non-halting behavior Kaz Kylheku <643-408-1753@kylheku.com> - 2025-10-21 03:06 +0000
                Re: HHH(DD) Input exactly matches non-halting behavior olcott <polcott333@gmail.com> - 2025-10-20 22:18 -0500
                Re: HHH(DD) Input exactly matches non-halting behavior Kaz Kylheku <643-408-1753@kylheku.com> - 2025-10-21 03:30 +0000
                Re: HHH(DD) Input exactly matches non-halting behavior olcott <polcott333@gmail.com> - 2025-10-20 22:39 -0500
                Re: HHH(DD) Input exactly matches non-halting behavior Kaz Kylheku <643-408-1753@kylheku.com> - 2025-10-21 05:38 +0000
      Re: My two specifications are equivalent HHH(DD)==0 is correct Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-10-20 12:09 +0100
        Re: My two specifications are equivalent HHH(DD)==0 is correct Richard Heathfield <rjh@cpax.org.uk> - 2025-10-20 12:49 +0100
          Re: My two specifications are equivalent HHH(DD)==0 is correct olcott <polcott333@gmail.com> - 2025-10-20 12:10 -0500
  Re: My two specifications are equivalent HHH(DD)==0 is correct Mikko <mikko.levanto@iki.fi> - 2025-10-19 14:03 +0300
    Re: My two specifications are equivalent HHH(DD)==0 is correct olcott <polcott333@gmail.com> - 2025-10-19 11:28 -0500

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