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Re: The halting problem is self-contradictory

From Kaz Kylheku <643-408-1753@kylheku.com>
Newsgroups comp.theory
Subject Re: The halting problem is self-contradictory
Date 2025-10-15 20:47 +0000
Organization A noiseless patient Spider
Message-ID <20251015133621.400@kylheku.com> (permalink)
References (4 earlier) <10cn5ej$3dfdk$1@dont-email.me> <20251014213152.861@kylheku.com> <10co1fk$3kki0$1@dont-email.me> <20251015092748.515@kylheku.com> <10cos3j$3t2ub$1@dont-email.me>

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On 2025-10-15, olcott <polcott333@gmail.com> wrote:
> Please think this all the way through without making any guesses.
>
> Simulating Termination Analyzer HHH correctly simulates its input until:

This sentence must end with nothing other than "until that input terminates".

Otherwise the simulation is not complete and correct.

> (a) Detects a non-terminating behavior pattern:
>      abort simulation and return 0.
> (b) Simulated input reaches its simulated "return" statement:
>      return 1.
> (c) If HHH must abort its simulation to prevent its own non-termination
>      then HHH is correct to abort this simulation and return 0.

HHH is correct to abort the simulation because if it doesn't do that,
it will not terminate. All halting deciders that incorporate simulation
as a tool must break out of simulation at some point in order not to be
tripped up by inputs that fail to terminate.

Without breaking out of the simulation, it would not be possible
for HHH(Infinite_Loop) or HHH(Infinite_Recursion) to decide correctly
that the return value should be zero.

However, nothing is effective against the diagonal input.

> What value should HHH(DD) correctly return?

The set of possible solutions is the empty set.

   3x +  y = 5
   6x + 2y = 3

What pairs <x, y> satisfy these equations?

HHH(DD) not having a solution is no different from simultaneous
equations in n variables not having a solution.

Elementary school children can work with these.

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

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The halting problem is self-contradictory olcott <polcott333@gmail.com> - 2025-10-14 21:17 -0500
  Re: The halting problem is self-contradictory Kaz Kylheku <643-408-1753@kylheku.com> - 2025-10-15 02:46 +0000
    Re: The halting problem is self-contradictory olcott <polcott333@gmail.com> - 2025-10-14 22:04 -0500
      Re: The halting problem is self-contradictory Kaz Kylheku <643-408-1753@kylheku.com> - 2025-10-15 03:34 +0000
        Re: The halting problem is self-contradictory olcott <polcott333@gmail.com> - 2025-10-14 22:46 -0500
          Re: The halting problem is self-contradictory Kaz Kylheku <643-408-1753@kylheku.com> - 2025-10-15 05:36 +0000
            Re: The halting problem is self-contradictory olcott <polcott333@gmail.com> - 2025-10-15 06:44 -0500
              Re: The halting problem is self-contradictory Kaz Kylheku <643-408-1753@kylheku.com> - 2025-10-15 16:38 +0000
                Re: The halting problem is self-contradictory olcott <polcott333@gmail.com> - 2025-10-15 12:12 -0500
                Re: The halting problem is self-contradictory Alan Mackenzie <acm@muc.de> - 2025-10-15 17:19 +0000
                Re: The halting problem is self-contradictory olcott <polcott333@gmail.com> - 2025-10-15 12:24 -0500
                Re: The halting problem is self-contradictory Alan Mackenzie <acm@muc.de> - 2025-10-15 18:25 +0000
                Re: The halting problem is self-contradictory olcott <polcott333@gmail.com> - 2025-10-15 14:07 -0500
                Re: The halting problem is self-contradictory Kaz Kylheku <643-408-1753@kylheku.com> - 2025-10-16 06:55 +0000
                Re: The halting problem is self-contradictory Richard Heathfield <rjh@cpax.org.uk> - 2025-10-16 08:33 +0100
                The Halting Problem is Incoherent olcott <polcott333@gmail.com> - 2025-10-16 08:23 -0500
                The Halting Problem is Incoherent olcott <polcott333@gmail.com> - 2025-10-15 14:14 -0500
                Re: The halting problem is self-contradictory Kaz Kylheku <643-408-1753@kylheku.com> - 2025-10-15 19:01 +0000
                The Halting Problem is Incoherent olcott <polcott333@gmail.com> - 2025-10-15 14:11 -0500
                Re: The halting problem is self-contradictory Kaz Kylheku <643-408-1753@kylheku.com> - 2025-10-15 18:54 +0000
                Re: The halting problem is self-contradictory olcott <polcott333@gmail.com> - 2025-10-15 14:19 -0500
                Re: The halting problem is self-contradictory "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-10-15 13:14 -0700
                Re: The halting problem is self-contradictory Kaz Kylheku <643-408-1753@kylheku.com> - 2025-10-15 20:47 +0000
                Re: The halting problem is self-contradictory olcott <polcott333@gmail.com> - 2025-10-15 16:00 -0500
                Re: The halting problem is self-contradictory olcott <polcott333@gmail.com> - 2025-10-15 17:18 -0500
                Re: The halting problem is self-contradictory Kaz Kylheku <643-408-1753@kylheku.com> - 2025-10-16 19:12 +0000
                Re: The halting problem is self-contradictory olcott <polcott333@gmail.com> - 2025-10-16 14:58 -0500
                Re: The halting problem is self-contradictory olcott <polcott333@gmail.com> - 2025-10-16 15:56 -0500
                Re: The halting problem is self-contradictory Alan Mackenzie <acm@muc.de> - 2025-10-16 21:07 +0000
                Re: The halting problem is self-contradictory olcott <polcott333@gmail.com> - 2025-10-16 16:19 -0500
                Re: The halting problem is self-contradictory Richard Heathfield <rjh@cpax.org.uk> - 2025-10-16 22:25 +0100
                Re: The halting problem is self-contradictory olcott <polcott333@gmail.com> - 2025-10-16 16:39 -0500
                Re: The halting problem is self-contradictory Kaz Kylheku <643-408-1753@kylheku.com> - 2025-10-16 21:46 +0000
                Re: The halting problem is self-contradictory Kaz Kylheku <643-408-1753@kylheku.com> - 2025-10-16 21:45 +0000
                The Halting Problem is Incoherent olcott <polcott333@gmail.com> - 2025-10-16 17:28 -0500
        Re: The halting problem is self-contradictory cross@spitfire.i.gajendra.net (Dan Cross) - 2025-10-15 12:21 +0000
          Re: The halting problem is self-contradictory olcott <polcott333@gmail.com> - 2025-10-15 07:32 -0500
            Re: The halting problem is self-contradictory tTh <tth@none.invalid> - 2025-10-15 16:50 +0200
            Re: The halting problem is self-contradictory Kaz Kylheku <643-408-1753@kylheku.com> - 2025-10-15 16:25 +0000
            Re: The halting problem is self-contradictory -- application to c/c++ Mikko <mikko.levanto@iki.fi> - 2025-10-16 12:34 +0300
              Re: The halting problem is self-contradictory -- application to c/c++ olcott <polcott333@gmail.com> - 2025-10-16 08:27 -0500
                Re: The halting problem is self-contradictory -- application to c/c++ "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-10-16 14:03 -0700
                Re: The halting problem is self-contradictory -- application to c/c++ Mikko <mikko.levanto@iki.fi> - 2025-10-17 11:45 +0300
                Re: The halting problem is self-contradictory -- application to c/c++ olcott <polcott333@gmail.com> - 2025-10-17 10:11 -0500
                Re: The halting problem is self-contradictory -- application to c/c++ Mikko <mikko.levanto@iki.fi> - 2025-10-18 11:58 +0300
                Re: The halting problem is self-contradictory -- application to c/c++ olcott <polcott333@gmail.com> - 2025-10-18 05:47 -0500
                Re: The halting problem is self-contradictory -- application to c/c++ Mikko <mikko.levanto@iki.fi> - 2025-10-19 11:39 +0300
                Re: The halting problem is self-contradictory -- application to c/c++ Richard Heathfield <rjh@cpax.org.uk> - 2025-10-19 10:31 +0100
                Re: The halting problem is self-contradictory -- application to c/c++ Mikko <mikko.levanto@iki.fi> - 2025-10-19 14:16 +0300
                Re: The halting problem is self-contradictory -- application to c/c++ Richard Heathfield <rjh@cpax.org.uk> - 2025-10-19 13:38 +0100
                Re: The halting problem is self-contradictory -- application to c/c++ olcott <polcott333@gmail.com> - 2025-10-19 11:04 -0500
                Re: The halting problem is self-contradictory -- application to c/c++ "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-10-19 13:22 -0700
                Re: The halting problem is self-contradictory -- application to c/c++ "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-10-19 13:34 -0700
        Re: The halting problem is self-contradictory olcott <polcott333@gmail.com> - 2025-10-14 23:00 -0500
      Re: The halting problem is self-contradictory Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-10-16 05:37 +0100
    Re: The halting problem is self-contradictory Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-10-15 05:39 +0100
      Re: The halting problem is self-contradictory Kaz Kylheku <643-408-1753@kylheku.com> - 2025-10-15 05:38 +0000
        The Halting Problem is Incoherent olcott <polcott333@gmail.com> - 2025-10-15 18:33 -0500
          Re: The Halting Problem is Incoherent Python <jpierre.messager@gmail.com> - 2025-10-15 23:59 +0000
          Re: The Halting Problem is Incoherent Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-10-16 06:46 +0100
            Re: The Halting Problem is Incoherent olcott <polcott333@gmail.com> - 2025-10-16 08:14 -0500
        Re: The halting problem is self-contradictory Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-10-16 05:53 +0100
          Re: The halting problem is self-contradictory olcott <polcott333@gmail.com> - 2025-10-16 07:56 -0500
  Re: The halting problem is self-contradictory Mikko <mikko.levanto@iki.fi> - 2025-10-15 12:15 +0300
    Re: The halting problem is self-contradictory olcott <polcott333@gmail.com> - 2025-10-15 07:30 -0500
      Re: The halting problem is self-contradictory Mikko <mikko.levanto@iki.fi> - 2025-10-16 12:21 +0300
        Re: The halting problem is self-contradictory olcott <polcott333@gmail.com> - 2025-10-16 08:34 -0500
          Re: The halting problem is self-contradictory Kaz Kylheku <643-408-1753@kylheku.com> - 2025-10-16 21:31 +0000
            The halting problem incoherent olcott <polcott333@gmail.com> - 2025-10-16 17:04 -0500
              Re: The halting problem incoherent Mikko <mikko.levanto@iki.fi> - 2025-10-17 11:59 +0300
                Re: The halting problem incoherent olcott <polcott333@gmail.com> - 2025-10-17 06:47 -0500
          Re: The halting problem is self-contradictory Mikko <mikko.levanto@iki.fi> - 2025-10-17 11:54 +0300
            Re: The halting problem is self-contradictory olcott <polcott333@gmail.com> - 2025-10-17 10:15 -0500
              Re: The halting problem is self-contradictory Mikko <mikko.levanto@iki.fi> - 2025-10-19 11:42 +0300
                Re: The halting problem is self-contradictory olcott <polcott333@gmail.com> - 2025-10-19 11:08 -0500
                Re: The halting problem is self-contradictory joes <noreply@example.org> - 2025-10-19 18:43 +0000
                Re: The halting problem is self-contradictory olcott <polcott333@gmail.com> - 2025-10-20 10:24 -0500
                Re: The halting problem is self-contradictory joes <noreply@example.org> - 2025-10-20 17:18 +0000
                Re: The halting problem is self-contradictory olcott <polcott333@gmail.com> - 2025-10-20 12:34 -0500
                Re: The halting problem is self-contradictory joes <noreply@example.org> - 2025-10-20 17:41 +0000
                Re: The halting problem is self-contradictory olcott <polcott333@gmail.com> - 2025-10-20 12:47 -0500
                Re: The halting problem is self-contradictory joes <noreply@example.org> - 2025-10-20 18:09 +0000
                Re: The halting problem is self-contradictory olcott <polcott333@gmail.com> - 2025-10-20 13:42 -0500
                Re: The halting problem is self-contradictory joes <noreply@example.org> - 2025-10-20 19:21 +0000
                Re: The halting problem is self-contradictory olcott <polcott333@gmail.com> - 2025-10-20 14:30 -0500
                Re: The halting problem is self-contradictory joes <noreply@example.org> - 2025-10-20 22:15 +0000
                Re: The halting problem is self-contradictory olcott <polcott333@gmail.com> - 2025-10-20 17:33 -0500
                Re: The halting problem is self-contradictory olcott <polcott333@gmail.com> - 2025-10-20 17:43 -0500
                Re: The halting problem is self-contradictory "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-10-20 15:59 -0700
                Re: The halting problem is self-contradictory Kaz Kylheku <643-408-1753@kylheku.com> - 2025-10-20 23:58 +0000
                Re: The halting problem is self-contradictory olcott <polcott333@gmail.com> - 2025-10-20 19:07 -0500
                Re: The halting problem is self-contradictory Kaz Kylheku <643-408-1753@kylheku.com> - 2025-10-21 01:32 +0000
                Re: The halting problem is self-contradictory olcott <polcott333@gmail.com> - 2025-10-20 20:38 -0500
                Re: The halting problem is self-contradictory Kaz Kylheku <643-408-1753@kylheku.com> - 2025-10-21 02:00 +0000
                Re: The halting problem is self-contradictory olcott <polcott333@gmail.com> - 2025-10-20 21:21 -0500
                Re: The halting problem is self-contradictory Kaz Kylheku <643-408-1753@kylheku.com> - 2025-10-21 03:22 +0000
                The Halting Problem is Incoherent olcott <polcott333@gmail.com> - 2025-10-20 22:37 -0500
                Re: The Halting Problem is Incoherent dbush <dbush.mobile@gmail.com> - 2025-10-20 23:45 -0400
                Re: The Halting Problem is Incoherent olcott <polcott333@gmail.com> - 2025-10-20 22:51 -0500
                Re: The Halting Problem is Incoherent dbush <dbush.mobile@gmail.com> - 2025-10-20 23:55 -0400
                Re: The Halting Problem is Incoherent olcott <polcott333@gmail.com> - 2025-10-20 23:09 -0500
                Re: The Halting Problem is Incoherent dbush <dbush.mobile@gmail.com> - 2025-10-21 08:09 -0400
                Re: The Halting Problem is Incoherent olcott <polcott333@gmail.com> - 2025-10-21 08:30 -0500
                Re: The Halting Problem is Incoherent dbush <dbush.mobile@gmail.com> - 2025-10-21 09:34 -0400
                Re: The Halting Problem is Incoherent olcott <polcott333@gmail.com> - 2025-10-21 09:45 -0500
                Re: The Halting Problem is Incoherent dbush <dbush.mobile@gmail.com> - 2025-10-21 10:51 -0400
                Re: The Halting Problem is Incoherent olcott <polcott333@gmail.com> - 2025-10-21 10:17 -0500
                Re: The Halting Problem is Incoherent dbush <dbush.mobile@gmail.com> - 2025-10-21 11:19 -0400
                Re: The Halting Problem is Incoherent olcott <polcott333@gmail.com> - 2025-10-23 10:26 -0500
                Re: The Halting Problem is Incoherent dbush <dbush.mobile@gmail.com> - 2025-10-23 11:31 -0400
                Re: The Halting Problem is Incoherent olcott <polcott333@gmail.com> - 2025-10-23 11:17 -0500
                Re: The Halting Problem is Incoherent dbush <dbush.mobile@gmail.com> - 2025-10-23 12:57 -0400
                Re: The Halting Problem is Incoherent Kaz Kylheku <643-408-1753@kylheku.com> - 2025-10-21 05:42 +0000
                Re: The Halting Problem is Incoherent Richard Heathfield <rjh@cpax.org.uk> - 2025-10-21 06:55 +0100
                Re: The Halting Problem is Incoherent olcott <polcott333@gmail.com> - 2025-10-21 01:37 -0500
                Re: The Halting Problem is Incoherent Kaz Kylheku <643-408-1753@kylheku.com> - 2025-10-21 16:22 +0000
                Re: The halting problem is self-contradictory olcott <polcott333@gmail.com> - 2025-10-20 20:55 -0500
                Re: The halting problem is self-contradictory Kaz Kylheku <643-408-1753@kylheku.com> - 2025-10-21 02:15 +0000
                Re: The halting problem is self-contradictory olcott <polcott333@gmail.com> - 2025-10-20 22:02 -0500
                Re: The halting problem is self-contradictory Kaz Kylheku <643-408-1753@kylheku.com> - 2025-10-20 20:59 +0000
                Re: The halting problem is self-contradictory Mikko <mikko.levanto@iki.fi> - 2025-10-20 12:22 +0300
                Re: The halting problem is self-contradictory olcott <polcott333@gmail.com> - 2025-10-20 12:06 -0500
                Re: The halting problem is self-contradictory Mikko <mikko.levanto@iki.fi> - 2025-10-22 11:51 +0300
                Re: The halting problem is self-contradictory olcott <polcott333@gmail.com> - 2025-10-22 07:22 -0500
                Re: The halting problem is self-contradictory Mikko <mikko.levanto@iki.fi> - 2025-10-23 13:04 +0300
    Re: The halting problem is self-contradictory "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-10-15 13:08 -0700
  Re: The halting problem is self-contradictory Richard Damon <Richard@Damon-Family.org> - 2025-10-16 07:55 -0400

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