Getting around the Halting Problem
Logic in Computer Science
2022-08-11 v8
Abstract
There are numbers k and s and a URM program A(n,m) satisfying the following conditions. 1. If A(n,m) halts, then Cn(m) diverges. 2. For all n, C_k(n) = A(n,n) and C_s(n) = C_k(s). 3. A(k,s) halts and for all n, A(s,n) diverges. Here C_n(_) is a program with index n in some exhaustive enumeration of all possible programs. This has implications for solving the liar paradox and for generalization of G\"odel incompleteness theorem to formal systems other than PA.
Keywords
Cite
@article{arxiv.1706.03392,
title = {Getting around the Halting Problem},
author = {X. Y. Newberry},
journal= {arXiv preprint arXiv:1706.03392},
year = {2022}
}