Combinatorial enumeration of groups, graphs, and chemical compounds
Combinatorial enumeration of groups, graphs, and chemical compounds
Models of massive parallelism: analysis of cellular automata and neural networks
Models of massive parallelism: analysis of cellular automata and neural networks
Finite fields
Simulations between cellular automata on Cayley graphs
Theoretical Computer Science
Two-dimensional cellular automata and their neighborhoods
Theoretical Computer Science
Information dynamics of cellular automata I: an algebraic study
Fundamenta Informaticae - Special issue on cellular automata
Theory of Self-Reproducing Automata
Theory of Self-Reproducing Automata
Changing the neighborhood of cellular automata
MCU'07 Proceedings of the 5th international conference on Machines, computations, and universality
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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, &phis;) of ν and Q, respectively, such that (f B, ν B) = (&phis; −1 f A π&phis;, 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.