Automorphism Classification of Cellular Automata

• Autorzy: Nishio H.
• Języki publikacji: EN

Abstrakty

EN

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 v and state set Q. Two CA (Z^d, Q, f_A, .A) and (Z^d, Q, f_B, v_B) are called automorphic, if there is a pair of permutationsπ&pfi" of v and Q, respectively, such that (f_B, vB) = ([formula] where v^π denotes a permutation of v and f*π denotes a permutation of arguments of local function f corresponding to v*π This automorphism 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.

Słowa kluczowe

EN

cellular automation; automorphism; classification; permutations; neighborhood; group action; ECA

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2010
• Tom: Vol. 104, nr 1/2
• Strony: 125--140
• Opis fizyczny: Bibliogr. 22 poz., wykr.

Twórcy

autor

Nishio H.

• Kyoto University, Iwakura Miyake-cho 204-1, Sakyo-ku, 606-0022, Kyoto, Japan,

Bibliografia

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