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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. [ABSTRACT FROM AUTHOR]

Expressiveness and convergence of evolutionary computation (EC) is studied using the evolutionary automata model. It turns out that all standard classes of evolutionary automata are equally expressive when they operate in the terminal mode, i.e. in the terminal mode, evolutionary finite automata (EFA) are as expressive as evolutionary pushdown automata, evolutionary linearly bounded automata, evolutionary Turing machines or evolutionary inductive Turing machines. For example, the simplest class of evolutionary automata, EFA, can accept all recursively enumerable languages (i.e. EFA have power of Turing machines) and even more—they can accept languages that are not recursively enumerable. Due to utilization of evolutionary automata, we obtain also very simple sufficient conditions for convergence of EC. [ABSTRACT FROM PUBLISHER]

This paper presents a novel model for resource bounded computation based on process algebras. Such model is called the $-calculus (cost calculus). Resource bounded computation attempts to find the best answer possible given operational constraints. The $-calculus provides a uniform representation for optimization in the presence of limited resources. It uses cost-optimization to find the best quality solutions while using a minimal amount of resources. A unique aspect of the approach is to propose a resource bounded process algebra as a generic problem solving paradigm targeting interactive AI applications. The goal of the $-calculus is to propose a computational model with built-in performance measure as its central element. This measure allows not only the expression of solutions, but also provides the means to incrementally construct solutions for computationally hard, real-life problems. This is a dramatic contrast with other models like Turing machines, λ-calculus, or conventional process algebras. This highly expressive model must therefore be able to express approximate solutions. This paper describes the syntax and operational cost semantics of the calculus. A standard cost function has been defined for strongly and weakly congruent cost expressions. Example optimization problems are given which take into account the incomplete knowledge and the amount of resources used by an agent. The contributions of the paper are twofold: firstly, some necessary conditions for achieving global optimization by performing local optimization in time and/or space are found. That deals with incomplete information and complexity during problem solving. Secondly, developing an algebra which expresses current practices, e.g., neural nets, cellular automata, dynamic programming, evolutionary computation, or mobile robotics as limiting cases, provides a tool for exploring the theoretical underpinnings of these methods. As the result, hybrid methods can be naturally expressed and developed using the algebra. [ABSTRACT FROM AUTHOR]