1 research outputs found
On Completeness of Cost Metrics and Meta-Search Algorithms in \$-Calculus
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. We started the population process of these new classes. 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