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Cellular Automata Associated with Σ-Algebras
Shuichi INOKUCHI Hitoshi FURUSAWA Toshikazu ISHIDA Yasuo KAWAHARA
IEICE TRANSACTIONS on Information and Systems
Publication Date: 2016/03/01
Online ISSN: 1745-1361
Type of Manuscript: Special Section PAPER (Special Section on Foundations of Computer Science---Developments of the Theory of Algorithms and Computation---)
Cellular Automata, Σ-algebras, Hedlund's theorem,
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In this paper we present a novel treatment of cellular automata (CA) from an algebraic point of view. CA on monoids associated with Σ-algebras are introduced. Then an extension of Hedlund's theorem which connects CA associated with Σ-algebras and continuous functions between prodiscrete topological spaces on the set of configurations are discussed.