Isomorphisms of Additive Cellular Automata on Finite Groups

2008/11/29 by Bulitko, Valeriy
#Cellular Automata and Lattice Gases (nlin.CG) #FOS: Physical sciences

paper · doi:10.48550/arxiv.0812.0111

Abstract

We study sources of isomorphisms of additive cellular automata on finite groups (called index-group). It is shown that many isomorphisms (called regular) of automata are reducible to the isomorphisms of underlying algebraic structures (such as the index-group, monoid of automata rules, and its subgroup of reversible elements). However for some groups there exist not regular automata isomorphisms. A complete description of linear automorphisms of the monoid is obtained. These automorphisms cover the most part of all automata isomorphisms for small groups and are represented by reversible matrices M such that for any index-group circulant C the matrix M^-1CM is an index-group circulant.

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