On Completeness of Cost Metrics and Meta-Search Algorithms in $-Calculus
Abstract
In the paper we define three new complexity classes for Turing Machine undecidable problems inspired by the famous Cook/Levin's NP-complete complexity class for intractable problems. These are U-complete (Universal complete), D-complete (Diagonalization complete) and H-complete (Hypercomputation complete) classes. In the paper, in the spirit of Cook/Levin/Karp, we started the population process of these new classes assigning several undecidable problems to them. We justify that some super-Turing models of computation, i.e., models going beyond Turing machines, are tremendously expressive and they allow to accept arbitrary languages over a given alphabet including those undecidable ones. We prove also that one of such super-Turing models of computation - the $-Calculus, designed as a tool for automatic problem solving and automatic programming, has also such tremendous expressiveness. We investigate also completeness of cost metrics and meta-search algorithms in $-calculus.
Keywords
Cite
@article{arxiv.2106.15969,
title = {On Completeness of Cost Metrics and Meta-Search Algorithms in $-Calculus},
author = {Eugene Eberbach},
journal= {arXiv preprint arXiv:2106.15969},
year = {2023}
}