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Identification of probabilistic cellular automata

Billings, S.A. and Yang, Y.X. (2003) Identification of probabilistic cellular automata. IEEE Transactions on Systems Man and Cybernetics Part B: Cybernetics, 33 (2). pp. 225-236. ISSN 1083-4419


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The identification of probabilistic cellular automata (PCA) is studied using a new two stage neighborhood detection algorithm. It is shown that a binary probabilistic cellular automaton (BPCA) can be described by an integer-parameterized polynomial corrupted by noise. Searching for the correct neighborhood of a BPCA is then equivalent to selecting the correct terms which constitute the polynomial model of the BPCA, from a large initial term set. It is proved that the contribution values for the correct terms can be calculated independently of the contribution values for the noise terms. This allows the neighborhood detection technique developed for deterministic rules in to be applied with a larger cutoff value to discard the majority of spurious terms and to produce an initial presearch for the BPCA neighborhood. A multiobjective genetic algorithm (GA) search with integer constraints is then evolved to refine the reduced neighborhood and to identify the polynomial rule which is equivalent to the probabilistic rule with the largest probability. A probability table representing the BPCA can then be determined based on the identified neighborhood and the deterministic rule. The new algorithm is tested over a large set of one-dimensional (1D), two-dimensional (2D), and three-dimensional (3D) BPCA rules. Simulation results demonstrate the efficiency of the new method.

Item Type: Article
Copyright, Publisher and Additional Information: Copyright © 2003 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
Keywords: genetic algorithms, identification, probabilistic cellular automata, spatio–temporal systems
Institution: The University of Sheffield
Academic Units: The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Automatic Control and Systems Engineering (Sheffield)
Depositing User: Sherpa Assistant
Date Deposited: 02 Dec 2005
Last Modified: 04 Jun 2014 18:37
Published Version: http://dx.doi.org/10.1109/TSMCB.2003.810437
Status: Published
Refereed: Yes
Identification Number: 10.1109/TSMCB.2003.810437
URI: http://eprints.whiterose.ac.uk/id/eprint/790

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