Abstract : For any group G and set A, a cellular automaton over G and A is a transformation defined via a finite neighbourhood (called a memory set of ) and a local function . In this paper, we assume that G and A are both finite and study various algebraic properties of the finite monoid consisting of all cellular automata over G and A. Let G and A. In the first part, using information on the conjugacy classes of subgroups of G, we give a detailed description of the structure of in terms of direct and wreath products. In the second part, we study generating sets of . In particular, we prove that cannot be generated by cellular automata with small memory set, and, when G is finite abelian, we determine the minimal size of a set such that .
Matthew Cook; Turlough Neary. 22th International Workshop on Cellular Automata and Discrete Complex Systems (AUTOMATA), Jun 2016, Zurich, Switzerland. Lecture Notes in Computer Science, LNCS-9664, pp.90-104, 2016, Cellular Automata and Discrete Complex Systems. 〈10.1007/978-3-319-39300-1_8〉
https://hal.inria.fr/hal-01435036
Contributeur : Hal Ifip
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Dernière modification le : jeudi 19 juillet 2018 - 16:58:10
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Alonso Castillo-Ramirez, Maximilien Gadouleau. On Finite Monoids of Cellular Automata. Matthew Cook; Turlough Neary. 22th International Workshop on Cellular Automata and Discrete Complex Systems (AUTOMATA), Jun 2016, Zurich, Switzerland. Lecture Notes in Computer Science, LNCS-9664, pp.90-104, 2016, Cellular Automata and Discrete Complex Systems. 〈10.1007/978-3-319-39300-1_8〉. 〈hal-01435036〉
