Is the Halting problem effectively solvable non-algorithmically, and is the Goedel sentence in NP, but not in P?
General Mathematics
2007-05-23 v1
Abstract
We consider the thesis that an arithmetical relation, which holds for any, given, assignment of natural numbers to its free variables, is Turing-decidable if, and only if, it is the standard representation of a PA-provable formula. We show that, classically, such a thesis is, both, unverifiable and irrefutable, and, that it implies the Turing Thesis is false; that Goedel's arithmetical predicate R(x), treated as a Boolean function, is in the complexity class NP, but not in P; and that the Halting problem is effectively solvable, albeit not algorithmically.
Cite
@article{arxiv.math/0506126,
title = {Is the Halting problem effectively solvable non-algorithmically, and is the Goedel sentence in NP, but not in P?},
author = {Bhupinder Singh Anand},
journal= {arXiv preprint arXiv:math/0506126},
year = {2007}
}
Comments
12 pages; an HTML version is available at http://alixcomsi.com/Is_the_Halting_problem.htm