On Completeness of Cost Metrics and Meta-Search Algorithms in $-Calculus

Eugene Eberbach

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arXiv · 2106.15969

On Completeness of Cost Metrics and Meta-Search Algorithms in $-Calculus

Eugene Eberbach

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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.

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Eugene Eberbach. 2021-06-30. On Completeness of Cost Metrics and Meta-Search Algorithms in $-Calculus. https://arxiv.org/abs/2106.15969

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