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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 20:47 +0000
Organization A noiseless patient Spider
Message-ID <20251020133542.246@kylheku.com> (permalink)
References (2 earlier) <10d2u4s$2iusp$1@dont-email.me> <10d4vr9$32t2d$1@dont-email.me> <10d5m9u$3aj68$3@dont-email.me> <20251020115253.395@kylheku.com> <10d61t7$3east$1@dont-email.me>

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On 2025-10-20, olcott <polcott333@gmail.com> wrote:
> On 10/20/2025 2:03 PM, Kaz Kylheku wrote:
>> On 2025-10-20, olcott <polcott333@gmail.com> wrote:
>>> On 10/20/2025 4:36 AM, joes wrote:
>>>> Am Sun, 19 Oct 2025 09:55:22 -0500 schrieb olcott:
>>>>
>>>>> If you understand the language well enough you will understand that the
>>>>> only way that HHH(DD) would terminate is out-of-memory error. This *does
>>>>> not count as halting*
>>>>> #define ENABLE_ABORT_CODE 1 When commented out HHH(DD) does not halt.
>>>> Yeah, but that’s a different program. The input does not have that
>>>> commented out.
>>>>
>>>
>>> When a halt decider must correctly predict the behavior
>>> that an non-halting input would have if not aborted there
>>> are always two programs and one of them is hypothetical.
>> 
>> No, both programs are real and can be constructed.
>> 
>> Your HHH is reporting on the wrong one. It is asked to analyze
>> a terminating one, but you're hypothesizing that it's still
>> making a remark on that other non-terminating one.
>> 
>
><Input to LLM systems>
> Please think this all the way through without making any guesses

You literally don't know what it looks like to think it through without
making any guesses. You cannot tell the difference.

> 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.

 (d) The input is non-terminating in a way that evades detection
     by the decider, so that the decider fails to terminate.

It is the mark of the idiot programmer to be missing important cases
in their case analysis.

Alan Perlis Epigram #32: "Programmers are not to be measured by their
ingenuity and their logic but by the completeness of their case
analysis."

Your case (a) happens for HHH(Infinite_Loop) and
HHH(Infinite_Recursion).

Case (b) happens for HHH(Terminator) which is defined as
void Terminator() {  }

Case (c) happens for HHH(DD) where DD is
void DD() { if HHH(DD) for(;;); }

Case (d) happens for some unspecified programs we have not
explored. (That is an understandable consequence of HHH not being a
proper decider for programs at large, focused only on the diagonal
cases; we need to mention this case for completeness!)

> Thus when the behavior of the input to HHH(DD)
> exactly matches the definition of non-halting then
> this input (not anything else in the universe)
> does specify non-halting behavior.

It doesn't, though. It is /impossible/ for HHH to encode a correct
definition of non-halting of DD. No matter how complicated you make HHH,
it will fall short on DD.

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

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Thread

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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