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On Finite Monoids of Cellular Automata
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 .
Cited literature [12 references]
https://hal.inria.fr/hal-01435036
Contributor : Hal Ifip <>
Submitted on : Friday, January 13, 2017 - 3:24:12 PM
Last modification on : Thursday, July 19, 2018 - 4:58:10 PM
Long-term archiving on: : Friday, April 14, 2017 - 8:30:52 PM
Contributor : Hal Ifip <>
Submitted on : Friday, January 13, 2017 - 3:24:12 PM
Last modification on : Thursday, July 19, 2018 - 4:58:10 PM
Long-term archiving on: : Friday, April 14, 2017 - 8:30:52 PM
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395687_1_En_8_Chapter.pdf
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