Papers by Eugene Eberbach
Evolutionary Automata: Expressiveness and Convergence of Evolutionary Computation
The Computer Journal, Sep 29, 2011
ABSTRACT Expressiveness and convergence of evolutionary computation (EC) is studied using the evo... more ABSTRACT 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.
Algorithms with Possibilities of Selflearning and Selfmodification
Fundamenta Informaticae, 1983
This paper concerns a concept of selfperfecting and selflearning of digital computer systems. Thi... more This paper concerns a concept of selfperfecting and selflearning of digital computer systems. This idea is not new, but continuously in the state of elaborations. Such systems, i.e. with a possibility of selflearning and selfmodification would have undoubtedly greater possibilities and elastic properties in their behaviour than traditional digital systems. In the paper a digital system is treated as a complex system of algorithms. As an abstract model of real algorithms. so called Mazurkiewicz FC-algorithm is considered. FC-algorithms used in the paper have been extended to modifiable Fe-algorithms by adding a time-variant structure and the use of the notion of tolerance spaces. This structure allowed us to introduce a model of learning for modifiable FC-algorithms. Learning is understood as a goal directed process of changes of activities on the basis of experience.
Semal: A Cost Language Based on the Calculus of Self-Modifiable Algorithms
International Journal of Software Engineering and Knowledge Engineering, Sep 1, 1994
The design, specification, and preliminary implementation of the SEMAL language, based upon the C... more The design, specification, and preliminary implementation of the SEMAL language, based upon the Calculus of Self-modifiable Algorithms model of computation is presented. A Calculus of Self-modifiable Algorithms is a universal theory for parallel and intelligent systems, integrating different styles of programming, and applied to a wealth of domains of future generation computers. It has some features from logic, rule-based, procedural, functional, and object-oriented programming. It has been designed to be a relatively universal tool for AI similar to the way Hoare’s Communicating Sequential Processes and Milner’s Calculus of Communicating Systems are basic theories for parallel systems. The formal basis of this approach is described. The model is used to derive a new programming paradigm, so-called cost languages and new computer architectures cost-driven computers. As a representative of cost languages, the SEMAL language is presented.
The calculus of self-modifiable algorithm based evolutionary computer network routing
Springer eBooks, 1995
ABSTRACT
EPiC series in computing, Jan 23, 2018
In the paper we prove in a new and simple way that Interaction machines are more powerful than Tu... more In the paper we prove in a new and simple way that Interaction machines are more powerful than Turing machines. To do that we extend the definition of Interaction machines to multiple interactive components, where each component may perform simple computation. The emerging expressiveness is due to the power of interaction and allows to accept languages not accepted by Turing machines. The main result that Interaction machines can accept arbitrary languages over a given alphabet sheds a new light to the power of interaction. Despite of that we do not claim that Interaction machines are complete. We claim that a complete theory of computer science cannot exist and especially, Turing machines or Interaction machines cannot be a complete model of computation. However complete models of computation may and should be approximated indefinitely and our contribution presents one of such attempts.
International Journal of Approximate Reasoning, Oct 1, 2008
In this paper, we generalize the utility theory to allow to use various performance measures, inc... more In this paper, we generalize the utility theory to allow to use various performance measures, including utilities, costs and fitness, and probability theory we extend to uncertainty theory, including probabilities, fuzzy sets and rough sets. The decision theory is defined typically as the combination of utility theory and probability theory. We generalize the decision theory as the performance measure theory and uncertainty theory. Bounded rational agents look for approximate optimal decisions under bounded resources and uncertainty. The $-calculus process algebra for problem solving applies the cost performance measures to converge to optimal solutions with minimal problem solving costs, and allows to incorporate probabilities, fuzzy sets and rough sets to deal with uncertainty and incompleteness. The approach is illustrated to find the optimal solutions with or without uncertainty. The same approach can be used to find solutions of the totally optimization problem, representing the tradeoff between the best quality and least costly solutions.
Ubiquity, Aug 1, 2012
Investigation of the essence and inherent traits of computation as a basic technological process ... more Investigation of the essence and inherent traits of computation as a basic technological process in contemporary society have attracted many researchers (cf., for example, Denning [1]; and Dodig--Crnkovic and Burgin ). Some did this in an informal setting based on computational and research practice, as well as on philosophical and methodological considerations. Others strived to build adequate mathematical models, assuming that similar to any mature science, computer science could efficiently study its complex objects only by means of mathematics. However, despite all the interest in this problem, the conception of computation remains too vague and ambiguous. For instance, in the computer science community, there is no consensus whether computation is a technological process or it exists in nature or whether Turing machines give an absolute model for computation or there are computing devices more powerful than Turing machines. As we are still far from a sufficient understanding of computation, and we know even less about evolutionary computation, it looks reasonable for the participants of our Symposium to base their answers on the following methodological considerations. Assuming evolutionary computation is a kind of computation, it is possible to base our understanding of evolutionary computation on one of the three premises. First, it is possible to assume we know/understand what computation is and to explain what specific characteristics differentiate evolutionary computation, finding its distinctions from the general case of computation. Second, it is possible to explore the problem from scratch, aiming at independent portrayal of evolutionary computation. Third, it is possible to elaborate an understanding of evolutionary computation based on some definition of computation chosen by the author. Note that genetic computations are a particular case of evolutionary computations.
Theoretical Computer Science, Sep 1, 2007
The $-calculus is the extension of the π -calculus, built around the central notion of cost and a... more The $-calculus is the extension of the π -calculus, built around the central notion of cost and allowing infinity in its operators. We propose the $-calculus as a more complete model for problem solving to provide a support to handle intractability and undecidability. It goes beyond the Turing Machine model. We define the semantics of the $-calculus using a novel optimization method (the kΩ -optimization), which approximates a nonexisting universal search algorithm and allows the simulation of many other search methods. In particular, the notion of total optimality has been utilized to provide an automatic way to deal with intractability of problem solving by optimizing together the quality of solutions and search costs. The sufficient conditions needed for completeness, optimality and total optimality of problem solving search are defined. A very flexible classification scheme of problem solving methods into easy, hard and solvable in the limit classes has been proposed. In particular, the third class deals with non-recursive solutions of undecidable problems. The approach is illustrated by solutions of some intractable and undecidable problems. We also briefly overview two possible implementations of the $-calculus.
In this paper we present a unified view of AI inspired by ideas from Evolutionary Computation as ... more In this paper we present a unified view of AI inspired by ideas from Evolutionary Computation as design of bounded rational agents. The approach specifies optimal programs rather than optimal actions, and is based on process algebras and anytime algorithms. The search method described in this paper is so general than many other search algorithms, including evolutionary search methods, become its special case. In this paper, we present a practical design of the programming language and environment targetting real-time complex domains. As AI systems move into more complex domains, all problems become real-time, because the agent will never have long enough time to solve the decision problem exactly.
Evolutionary Computation has been used traditionally for solution of hard optimization problems. ... more Evolutionary Computation has been used traditionally for solution of hard optimization problems. In a general case, solutions found by evolutionary algorithms are satis cing given current resources and constraints, but not necessary optimal. Under some conditions evolutionary algorithms are guaranteed (in in nity) to nd an optimal solution. However, evolutionary techniques are helpful not only to deal with intractable problems. In this paper we demonstrate, that EC is not restricted to algorithmic methods, and is more expressive than Turing Machines.
Ubiquity, Dec 1, 2013
Inconsistent Knowledge Systems. His recent publications include such books as "Theory of Informat... more Inconsistent Knowledge Systems. His recent publications include such books as "Theory of Information" (2010), "Measuring Power of Algorithms, Computer Programs, and Information Automata" (2010), and "Super--recursive Algorithms" (2005). He originated such theories as the general theory of information, mathematical theory of technology, system theory of time, theory of logical varieties, theory of named sets and neoclassical analysis (in mathematics) and made essential contributions to such fields as foundations of computer science, theory of algorithms and computation, information theory, theory of knowledge, theory of negative probabilities, theory of intellectual activity, and complexity studies.
It is interesting that typically in the proof of convergence of evolutionary algorithms only elit... more It is interesting that typically in the proof of convergence of evolutionary algorithms only elitist selection is considered. In this paper, we stress out that truly in reaching optimum of the fitness function completeness of search plays probably even more important role. The elitist selection helps in reaching the optimum. It allows to converge faster and not to lose the optimum in cases when we are uncertain that the optimum has been reached. An evolutionary search using elitist selection, but being incomplete, will not reach the optimum. This paper provides sufficient conditions for finding the best (optimal) solutions, or the best (totally optimal) solutions with minimal search costs. To do that we utilitze a new formal model of evolutionary computation, the Evolutionary Turing Machine. The results are applicable both to genetic algorithms, genetic programming, evolution strategies and evolutionary programming. The problem of finding total optimum, optimizing together the quality of solution together with an evolutionary algorithm is considered as a multiobjective optimization allowing to tackle real-world problems where the complexity of evolutionary search becomes an issue. A new classification of evolutionary procedures into easy, hard, and solvable in the limit classes, is proposed.
Evolutionary Automata and Deep Evolutionary Computing
The $-Calculus Process Algebra for Problem Solving and its Support for Bioinformatics
Indian International Conference on Artificial Intelligence, 2005
ABSTRACT In this paper a new technique for the solutions of hard computa- tional problems in bioi... more ABSTRACT In this paper a new technique for the solutions of hard computa- tional problems in bioinformatics is investigated. This is the $-calculus process algebra for problem solving that applies the cost performance measures to con- verge to optimal solutions with minimal problem solving costs. We demon- strate that the $-calculus generic search method, called the kΩ-optimization, can be used to solve gene finding and sequence alignment problems. The solu- tions can be either precise or approximate by applying the $-calculus optimiza- tion or total optimization.
Beyond Turing Machines
Bulletin of The European Association for Theoretical Computer Science, 2003
... Beyond Turing Machines [25 citations 3 self]. Download: http://www.cis. umassd.edu/~eeberba... more ... Beyond Turing Machines [25 citations 3 self]. Download: http://www.cis. umassd.edu/~eeberbach/papers/Beyond CACHED: Download as a PDF. by Eugene Eberbach , Peter Wegner. Add To MetaCart. ...
Theory and Applications of Mathematics & Computer Science, Apr 1, 2015
The $-calculus process algebra for problem solving applies the cost performance measures to conve... more The $-calculus process algebra for problem solving applies the cost performance measures to converge in finite time or in the limit to optimal solutions with minimal problem solving costs. The $-calculus belongs to superTuring models of computation. Its main goal is to provide the support to solve hard computational problems. It allows also to solve in the limit some undecidable problems. In the paper we demonstrate how to solve in the limit Turing Machine Halting Problem, to approximate the universal search algorithm, to decide diagonalization language, nontrivial properties of recursively enumerable languages, and how to solve Post Correspondence Problem and Busy Beaver Problem.
Algorithms with Possibilities of Selflearning and Selfmodification
Fundamenta Informaticae, 1983
This paper concerns a concept of selfperfecting and selflearning of digital computer systems. Thi... more This paper concerns a concept of selfperfecting and selflearning of digital computer systems. This idea is not new, but continuously in the state of elaborations. Such systems, i.e. with a possibility of selflearning and selfmodification would have undoubtedly greater possibilities and elastic properties in their behaviour than traditional digital systems. In the paper a digital system is treated as a complex system of algorithms. As an abstract model of real algorithms. so called Mazurkiewicz FC-algorithm is considered. FC-algorithms used in the paper have been extended to modifiable Fe-algorithms by adding a time-variant structure and the use of the notion of tolerance spaces. This structure allowed us to introduce a model of learning for modifiable FC-algorithms. Learning is understood as a goal directed process of changes of activities on the basis of experience.
Evolutionary Automata: Expressiveness and Convergence of Evolutionary Computation
The Computer Journal, 2011
ABSTRACT Expressiveness and convergence of evolutionary computation (EC) is studied using the evo... more ABSTRACT 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.
Eberbach E., Self-Modifiable Algorithms: Towards a Theory of Artificial Intelligence
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Papers by Eugene Eberbach