Additive cellular automata and algebraic series

B. Litow Philippe Dumas 1
1 ALGO - Algorithms
Inria Paris-Rocquencourt
Abstract : A cellular automaton is an array of regularly interconnected identical cells. We study here the special case of automata where each cell depends in additive manner on its neighbours. The successives states of a given cell form a sequence whose generating series proved to be always an algebric series. We also examplify the realization of a given algebraic series by means of an automaton. As a by product we obtain a relation between additive cellular automata and certain "automatic sequences" like the paper folding sequence.
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Submitted on : Wednesday, May 24, 2006 - 4:50:05 PM
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B. Litow, Philippe Dumas. Additive cellular automata and algebraic series. [Research Report] RR-1657, INRIA. 1992. ⟨inria-00074900⟩

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