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41
A Survey of Computational Complexity Results in Systems and Control
, 2000
"... The purpose of this paper is twofold: (a) to provide a tutorial introduction to some key concepts from the theory of computational complexity, highlighting their relevance to systems and control theory, and (b) to survey the relatively recent research activity lying at the interface between these fi ..."
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Cited by 116 (21 self)
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The purpose of this paper is twofold: (a) to provide a tutorial introduction to some key concepts from the theory of computational complexity, highlighting their relevance to systems and control theory, and (b) to survey the relatively recent research activity lying at the interface between these fields. We begin with a brief introduction to models of computation, the concepts of undecidability, polynomial time algorithms, NPcompleteness, and the implications of intractability results. We then survey a number of problems that arise in systems and control theory, some of them classical, some of them related to current research. We discuss them from the point of view of computational complexity and also point out many open problems. In particular, we consider problems related to stability or stabilizability of linear systems with parametric uncertainty, robust control, timevarying linear systems, nonlinear and hybrid systems, and stochastic optimal control.
A brief history of cellular automata
, 2000
"... Cellular automata are simple models of computation which exhibit fascinatingly complex behavior. They have captured the attention of several generations of researchers, leading to an extensive body of work. Here we trace a history of cellular automata from their beginnings with von Neumann to the pr ..."
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Cited by 46 (2 self)
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Cellular automata are simple models of computation which exhibit fascinatingly complex behavior. They have captured the attention of several generations of researchers, leading to an extensive body of work. Here we trace a history of cellular automata from their beginnings with von Neumann to the present day. The emphasis is mainly on topics closer to computer science and mathematics rather than physics, biology or other applications. The work should be of interest to both new entrants into the field as well as researchers working on particular aspects of cellular automata.
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 present ..."
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Cited by 32 (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
A Survey of ContinuousTime Computation Theory
 Advances in Algorithms, Languages, and Complexity
, 1997
"... Motivated partly by the resurgence of neural computation research, and partly by advances in device technology, there has been a recent increase of interest in analog, continuoustime computation. However, while specialcase algorithms and devices are being developed, relatively little work exists o ..."
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Cited by 29 (6 self)
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Motivated partly by the resurgence of neural computation research, and partly by advances in device technology, there has been a recent increase of interest in analog, continuoustime computation. However, while specialcase algorithms and devices are being developed, relatively little work exists on the general theory of continuoustime models of computation. In this paper, we survey the existing models and results in this area, and point to some of the open research questions. 1 Introduction After a long period of oblivion, interest in analog computation is again on the rise. The immediate cause for this new wave of activity is surely the success of the neural networks "revolution", which has provided hardware designers with several new numerically based, computationally interesting models that are structurally sufficiently simple to be implemented directly in silicon. (For designs and actual implementations of neural models in VLSI, see e.g. [30, 45]). However, the more fundamental...
Simulations of Graph Automata
 Proc. MFCS’98 Satellite Workshop on Cellular Automata
, 1998
"... We state a definition of the simulation of graph automata, which are machines built by putting copies of the same finitestate automaton at the vertices of a regular graph, reading the states of the neighbors. The graphs considered here are planar, with the elementary cycles of the same length, and ..."
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Cited by 17 (4 self)
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We state a definition of the simulation of graph automata, which are machines built by putting copies of the same finitestate automaton at the vertices of a regular graph, reading the states of the neighbors. The graphs considered here are planar, with the elementary cycles of the same length, and form regular tilings of the hyperbolic plane. Thereafter, we present some results of simulation between such graph automata, comparing them to the cellular automata on Cayley graphs, and we conclude with a possible speed hierarchy. 1 Introduction Since the beginning of the electronic computer era, di#erent machine models have existed, but while the classical sequential computer has been enormously developed, the intrinsic massive parallel models had a harder time to get o#, maybe because it is more di#cult for us to understand the behavior of such tools and to build and steer them correctly. However, several fundamental questions about the computing power of these models have been successfu...
Characterizing Configuration Spaces of Simple Threshold Cellular Automata
 in SpringerVerlag LNCS series
, 2004
"... Abstract. We study herewith the simple threshold cellular automata (CA), as perhaps the simplest broad class of CA with nonadditive (i.e., nonlinear and nonaffine) local update rules. We characterize all possible computations of the most interesting rule for such CA, namely, the Majority (MAJ) ru ..."
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Cited by 16 (5 self)
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Abstract. We study herewith the simple threshold cellular automata (CA), as perhaps the simplest broad class of CA with nonadditive (i.e., nonlinear and nonaffine) local update rules. We characterize all possible computations of the most interesting rule for such CA, namely, the Majority (MAJ) rule, both in the classical, parallel CA case, and in case of the corresponding sequential CA where the nodes update sequentially, one at a time. We compare and contrast the configuration spaces of arbitrary simple threshold automata in those two cases, and point out that some parallel threshold CA cannot be simulated by any of their sequential counterparts. We show that the temporal cycles exist only in case of (some) parallel simple threshold CA, but can never take place in sequential threshold CA. We also show that most threshold CA have very few fixed point configurations and few (if any) cycle configurations, and that, while the MAJ sequential and parallel CA may have many fixed points, nonetheless “almost all” configurations, in both parallel and sequential cases, are transient states. 1
Universality and decidability of numberconserving cellular automata
 THEORETICAL COMPUTER SCIENCE 292
, 2003
"... Numberconserving cellular automata (NCCA) are particularly interesting, both because of their natural appearance as models of real systems, and because of the strong restrictions that numberconservation implies. Here we extend the definition of the property to include cellular automata with any se ..."
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Cited by 14 (1 self)
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Numberconserving cellular automata (NCCA) are particularly interesting, both because of their natural appearance as models of real systems, and because of the strong restrictions that numberconservation implies. Here we extend the definition of the property to include cellular automata with any set of states n Z, and show that they can be always extended to “usual ” NCCA with contiguous states. We show a way to simulate any one dimensional CA through a one dimensional NCCA, proving the existence of intrinsically universal NCCA. Finally, we give an algorithm to decide, given a CA, if its states can be labeled with integers to produce a NCCA, and to find this relabeling if the answer is positive.
On Expressiveness of Evolutionary Computation: Is EC Algorithmic?
 Proc. 2002 World Congress on Computational Intelligence WCCI’2002
, 2002
"... Evolutionary Computation has been used traditionally for solution of hard optimization problems. In a general case, solutions found by evolutionary algorithms are satisficing given current resources and constraints, but not necessary optimal. Under some conditions evolutionary algorithms are guarant ..."
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Cited by 9 (4 self)
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Evolutionary Computation has been used traditionally for solution of hard optimization problems. In a general case, solutions found by evolutionary algorithms are satisficing given current resources and constraints, but not necessary optimal. Under some conditions evolutionary algorithms are guaranteed (in infinity) to find 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.
Expressiveness of $Calculus: What Matters?
 Advances in Soft Computing, Proc. of the 9th Intern. Symp. on Intelligent Information Systems IIS'2000, Bystra
, 2000
"... $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. $calculus has builtin costoptimizati ..."
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Cited by 7 (6 self)
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$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 investigate expressiveness of $calculus. We show that due to innitary means, it allows to express models having richer behavior than Turing machine, including cellular automata, interaction machines, neural networks, and random automata networks. We also investigate the importance of synchronization, representation of continuity, and higherorder.
On Parallel vs. Sequential Threshold Cellular Automata
 IN PROCEEDINGS OF THE FIRST EUROPEAN CONFERENCE ON COMPLEX SYSTEMS ECCS’05, EUROPEAN COMPLEX SYSTEMS SOCIETY
, 2005
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