Re: The error of the halting problem

On 6/4/2024 3:00 AM, Mikko wrote:

On 2024-06-03 20:53:01 +0000, olcott said:
 

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

 That does not identify which problem is meant by the term "halting problem",
nor does it identify what part of the problemis erroneous or what the
word "error" could even mean in this context, let alone how it would apply
to the particular unspecified point.
 

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