The error of the halting problem

From	olcott <polcott333@gmail.com>
Newsgroups	comp.theory, sci.logic
Subject	The error of the halting problem
Date	2024-06-03 15:53 -0500
Organization	A noiseless patient Spider
Message-ID	<v3lafd$1uml$1@dont-email.me> (permalink)

Cross-posted to 2 groups.

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For any program H that might determine whether programs halt, a
"pathological" program D, called with some input, can pass its own
source and its input to H and then specifically do the opposite of what
H predicts D will do. No H can exist that handles this case. 
https://en.wikipedia.org/wiki/Halting_problem

The way that the halting problem is conventionally understood is that H
must correctly answer yes or no to an input that contradicts both
answers, thus H is being asked a question isomorphic to the Liar
Paradox: Is this sentence true or false: "This sentence is not true." ?

*Two PhD computer science professors agree with this assessment*

E C R Hehner. Problems with the Halting Problem, COMPUTING2011 Symposium 
on 75 years of Turing Machine and Lambda-Calculus, Karlsruhe Germany, 
invited, 2011 October 20-21; Advances in Computer Science and 
Engineering v.10 n.1 p.31-60, 2013
https://www.cs.toronto.edu/~hehner/PHP.pdf

Bill Stoddart. The Halting Paradox
20 December 2017
https://arxiv.org/abs/1906.05340
arXiv:1906.05340 [cs.LO]

E C R Hehner. Objective and Subjective Specifications
WST Workshop on Termination, Oxford.  2018 July 18.
See https://www.cs.toronto.edu/~hehner/OSS.pdf


-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

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The error of the halting problem olcott <polcott333@gmail.com> - 2024-06-03 15:53 -0500
  Re: The error of the halting problem Richard Damon <richard@damon-family.org> - 2024-06-03 20:55 -0400
    Re: The error of the halting problem olcott <polcott333@gmail.com> - 2024-06-03 19:59 -0500
      Re: The error of the halting problem Richard Damon <richard@damon-family.org> - 2024-06-03 21:44 -0400
        Re: The error of the halting problem olcott <polcott333@gmail.com> - 2024-06-03 20:51 -0500
          Re: The error of the halting problem Richard Damon <richard@damon-family.org> - 2024-06-03 21:58 -0400
            Re: The error of the halting problem olcott <polcott333@gmail.com> - 2024-06-03 21:14 -0500
              Re: The error of the halting problem Richard Damon <richard@damon-family.org> - 2024-06-03 22:26 -0400
                Re: The error of the halting problem olcott <polcott333@gmail.com> - 2024-06-03 21:32 -0500
                Re: The error of the halting problem Richard Damon <richard@damon-family.org> - 2024-06-03 22:47 -0400
                Re: The error of the halting problem olcott <polcott333@gmail.com> - 2024-06-03 21:58 -0500
                Re: The error of the halting problem Richard Damon <richard@damon-family.org> - 2024-06-03 23:11 -0400
                Re: The error of the halting problem joes <noreply@example.com> - 2024-06-04 08:29 +0000
                Re: The error of the halting problem --- G is untrue in PA olcott <polcott333@gmail.com> - 2024-06-04 12:45 -0500
                Re: The error of the halting problem --- G is untrue in PA Richard Damon <richard@damon-family.org> - 2024-06-04 21:48 -0400
                Re: The error of the halting problem Mikko <mikko.levanto@iki.fi> - 2024-06-04 12:24 +0300
              Re: The error of the halting problem joes <noreply@example.com> - 2024-06-04 08:27 +0000
      Re: The error of the halting problem Mikko <mikko.levanto@iki.fi> - 2024-06-04 11:09 +0300
  Re: The error of the halting problem Mikko <mikko.levanto@iki.fi> - 2024-06-04 11:00 +0300
    Re: The error of the halting problem olcott <polcott333@gmail.com> - 2024-06-04 12:28 -0500
      Re: The error of the halting problem Richard Damon <richard@damon-family.org> - 2024-06-04 21:48 -0400

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