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

TL;DR
This paper introduces three new complexity classes for undecidable problems, explores super-Turing models like the $-Calculus, and analyzes the completeness of cost metrics and meta-search algorithms within this framework.
Contribution
It defines new complexity classes for undecidable problems and demonstrates the expressive power of super-Turing models like the $-Calculus.
Findings
Super-Turing models are highly expressive, accepting all languages including undecidable ones.
The $-Calculus has tremendous computational expressiveness.
Analysis of cost metrics and meta-search algorithms in $-Calculus shows their completeness.
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.…
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Taxonomy
TopicsComputability, Logic, AI Algorithms · Advanced Algebra and Logic · semigroups and automata theory
