Traced communication complexity of cellular automata

Authors:
Eric Goles;Pierre Guillon;Ivan Rapaport
Affiliations:
Facultad de Ingeniería y Ciencias Universidad Adolfo Ibañez, Santiago, Chile;DIM - CMM, UMI CNRS 2807, Universidad de Chile, Santiago, Chile and Department of Mathematics, University of Turku, Finland;DIM - CMM, UMI CNRS 2807, Universidad de Chile, Santiago, Chile
Venue:
Theoretical Computer Science
Year:
2011

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Abstract

We study cellular automata with respect to a new communication complexity problem: each of two players know half of some finite word, and must be able to tell whether the state of the central cell will follow a given evolution, by communicating as little as possible between each other. We present some links with classical dynamical concepts, especially equicontinuity, expansivity, entropy and give the asymptotic communication complexity of most elementary cellular automata.