Computational complexity of dynamical systems: The case of cellular automata

Authors:
P. Di Lena;L. Margara
Affiliations:
Department of Computer Science, University of Bologna, Mura Anteo Zamboni 7, 40127 Bologna, Italy;Department of Computer Science, University of Bologna, Mura Anteo Zamboni 7, 40127 Bologna, Italy
Venue:
Information and Computation
Year:
2008

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Abstract

Cellular Automata can be considered discrete dynamical systems and at the same time a model of parallel computation. In this paper we investigate the connections between dynamical and computational properties of Cellular Automata. We propose a classification of Cellular Automata according to the language complexities which rise from the basins of attraction of subshift attractors and investigate the intersection classes between our classification and other three topological classifications of Cellular Automata. From the intersection classes we can derive some necessary topological properties for a cellular automaton to be computationally universal according to our model.