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Beyond Turing Machines
"... In this paper we describe and analyze models of problem solving and computation going beyond Turing Machines. Three principles of extending the Turing Machine's expressiveness are identified, namely, by interaction, evolution and infinity. Several models utilizing the above principles are pr ..."
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Cited by 35 (4 self)
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In this paper we describe and analyze models of problem solving and computation going beyond Turing Machines. Three principles of extending the Turing Machine's expressiveness are identified, namely, by interaction, evolution and infinity. Several models utilizing the above principles are presented. Other
$Calculus Bounded Rationality = Process Algebra + Anytime Algorithms
 Applicable Mathematics: Its Perspectives and Challenges
, 2001
"... calculus is a higherorder polyadic process algebra with a utility (cost) integrating deliberative and reactive approaches for action selection in real time, and allowing to capture bounded optimization and metaresoning in distributed interactive AI systems. In this paper we present basic notions ..."
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Cited by 17 (13 self)
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calculus is a higherorder polyadic process algebra with a utility (cost) integrating deliberative and reactive approaches for action selection in real time, and allowing to capture bounded optimization and metaresoning in distributed interactive AI systems. In this paper we present basic notions of $calculus and demonstrate the versatility of its k\Omega metacontrol to plan behaviors for single and multiple agents. The approach can be understood as a generic proposal of a computational theory of AI based on search and optimization under bounded resources.
$Calculus of Bounded Rational Agents: Flexible Optimization as Search under Bounded Resources in Interactive Systems
 FUNDAMENTA INFORMATICAE
, 2005
"... This paper presents a novel model for resource bounded computation based on process algebras. ..."
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Cited by 7 (5 self)
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This paper presents a novel model for resource bounded computation based on process algebras.
Evolutionary Computation as a MultiAgent Search: a $Calculus Perspective for its Completeness and Optimality
 In Proceedings of Congress on Evolutionary Computation CEC’2001
, 2001
"... Evolutionary computation in its essense represents a multiagent competitive probabilistic search. It is useful for solutions of polynomial and hard optimization problems. The solutions found by evolutionary algorithms are not guaranteed to be optimal and evolutionary search is computationally very ..."
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Cited by 6 (3 self)
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Evolutionary computation in its essense represents a multiagent competitive probabilistic search. It is useful for solutions of polynomial and hard optimization problems. The solutions found by evolutionary algorithms are not guaranteed to be optimal and evolutionary search is computationally very expensive. Using a generic $calculus approach to AI, based on process algebras and anytime algorithms, we show that evolutionary search can be considered a special case of $calculus k\Omega search, and we present some results about completeness, optimality and search costs for evolutionary computation. The main result of the paper is to demonstrate how using $calculus to make evolutionary computation totally optimal, i.e., how to allow to find the best quality solution with minimal search cost. 1
Expressing Evolutionary Computation, Genetic Programming, Artif icial Life, Autonomous Agents and DNABased Computing in $Calculus  Revised Version
 in $Calculus, Proc. LateBreaking Papers of the Third Annual Genetic Programming Conf. GP98, Univ. of
, 2000
"... Genetic programming, autonomous agents, artif icial life and evolutionary computation share many common ideas. They generally investigate distributed complex processes, perhaps with the ability to interact. It seems to be natural to study their behavior using process algebras, which were designed to ..."
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Cited by 6 (5 self)
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Genetic programming, autonomous agents, artif icial life and evolutionary computation share many common ideas. They generally investigate distributed complex processes, perhaps with the ability to interact. It seems to be natural to study their behavior using process algebras, which were designed to handle distributed interactive systems. $calculus is a higherorder polyadic process algebra for resource bounded computation. It has been designed to handle autonomous agents, evolutionary computing, neural nets, expert systems, machine learning, and distributed interactive AI systems, in general. $calculus has builtin costoptimization mechanism allowing to deal with nondeterminism, incomplete and uncertain information. In this paper, we express in $calculus several subareas of evolutionary computation, including genetic programming, artif icial life, autonomous agents and DNAbased computing. 1
Challenges Facing Computer Science in the 21st Century
"... Some challenges facing computer science in the 21st century are presented. It is quite risky to foresee the longterm future and pose the correct list of problems for the science that is only 60 years old. Nevertheless it is very important to realize what has been achieved so far, and which probl ..."
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Some challenges facing computer science in the 21st century are presented. It is quite risky to foresee the longterm future and pose the correct list of problems for the science that is only 60 years old. Nevertheless it is very important to realize what has been achieved so far, and which problems are expected or is important to be solved in the near future. With this in mind, we present problems facing computer technology, architecture, distributed and parallel computing, programming paradigms, computational models and complexity, models of uncertainty, and artificial intelligence. We also try to provide some sociological, economical and political context associated with achievement of those objectives. Keywords: challenges, computer science, applied mathematics, 21st century 1 Introduction The Symposium is on Challenges in Mathematical Sciences for the New Millennium. Although mathematics is a well established and old (at least a few thousand years) science, the most chal...
doi:10.1093/comjnl/bxl062 Are There New Models of Computation? Reply to Wegner and Eberbach †
, 2007
"... Wegner and Eberbach have argued that there are fundamental limitations to Turing Machines as a foundation of computability and that these can be overcome by socalled superTuring models such as interaction machines, the pcalculus and the $calculus. In this article, we contest the Wegner and Eberb ..."
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Wegner and Eberbach have argued that there are fundamental limitations to Turing Machines as a foundation of computability and that these can be overcome by socalled superTuring models such as interaction machines, the pcalculus and the $calculus. In this article, we contest the Wegner and Eberbach claims. 1.
Expressiveness of the piCalculus and the $Calculus
"... Abstract: In this paper we investigate the expressiveness of two process algebras, the picalculus of mobile processes and the $calculus of bounded rational agents. We demonstrate that both models are more expressive than Turing Machines, i.e., they belong to superTuring models of computation. In ..."
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Abstract: In this paper we investigate the expressiveness of two process algebras, the picalculus of mobile processes and the $calculus of bounded rational agents. We demonstrate that both models are more expressive than Turing Machines, i.e., they belong to superTuring models of computation. In particular, they are able to solve the halting problem of the Universal Turing Machine. Additionally, the $calculus can approximate the solution of the universal search algorithm, and can simulate the picalculus, i.e., it is at least equally expressive as the picalculus.