Advances in the study of elementary cellular automata regular language complexity
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Artigo
Date
2016
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Complexity
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4
Authors
De Oliveira P.P.B.
Ruivo E.L.P.
Costa W.L.
Miki F.T.
Trafaniuc V.V.
Ruivo E.L.P.
Costa W.L.
Miki F.T.
Trafaniuc V.V.
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Journal Title
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Volume Title
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Abstract
© 2015 Wiley Periodicals, Inc.Cellular automata (CA) are discrete dynamical systems that, out of the fully local action of its state transition rule, are capable of generating a multitude of global patterns, from the trivial to the arbitrarily complex ones. The set of global configurations that can be obtained by iterating a one-dimensional cellular automaton for a finite number of times can always be described by a regular language. The size of the minimum finite automaton corresponding to such a language at a given time step provides a complexity measure of the underlying rule. Here, we study the time evolution of elementary CA, in terms of such a regular language complexity. We review and expand the original results on the topic, describe an alternative method for generating the subsequent finite automata in time, and provide a method to analyze and detect patterns in the complexity growth of the rules. © 2015 Wiley Periodicals, Inc. Complexity 21: 267–279, 2016.