Traced communication complexity of cellular automata☆

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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.

Keywords

Cellular automata
Communication complexity

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This work has been supported by the ECOS-Sud Project, Academy of Finland project 131558 (P. G.), Fondecyt 1070022, 1090156, BASAL-CMM (I. R.), Fondecyt 1100003, BASAL-CMM, Anillo Act88, SFI-Santa Fe (E. G.).

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