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- W1502875195 abstract "A new classification of arbitrary cellular automata (CA for short) in Z d is studied considering the set (group) of all permutations of the neighborhood ν and state set Q. Two CA (Z d, Q, f A, ν A) and (Z d, Q, f B, ν B) are called automorphisc, if there is a pair of permutations (π, p) of ν and Q, respectively, such that (f B, ν B) = (p −1 f A πp, ν A π), where ν π denotes a permutation of ν and f π denotes a permutation of arguments of local function f corresponding to ν π. This automorphissm naturally induces a classification of CA, such that it generally preserves the global properties of CA up to permutation. As a typical example of the theory, the local functions of 256 ECA (1-dimensional 3-nearest neighbors 2-states CA) are classified into 46 classes. We also give a computer test of surjectivity, injecitivity and reversibility of the classes." @default.
- W1502875195 created "2016-06-24" @default.
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- W1502875195 date "2010-01-01" @default.
- W1502875195 modified "2023-09-26" @default.
- W1502875195 title "Automorphissm Classification of Cellular Automata" @default.
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- W1502875195 doi "https://doi.org/10.3233/fi-2010-339" @default.
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