Internal symmetries of cellular automata.
(Internal) transformations on the space Sigma of automaton configurations are defined as bi-infinite sequences of permutations of the cell symbols. A pair of transformations (gamma,theta) is said to be an internal symmetry of a cellular automaton f:Sigma-->Sigma if f=theta(-1)fgamma. It is shown that the full group of internal symmetries of an automaton f can be encoded as a group homomorphism F such that theta=F(gamma). The domain and image of the homomorphism F have, in general, infinite order and F is presented by a local automaton-like rule. Algorithms to compute the symmetry homomorphism F and to classify automata by their symmetries are presented. Examples on the types of dynamical implications of internal symmetries are discussed in detail. (c) 1997 American Institute of Physics.
Urias
Jesus
J
Instituto de Investigacion en Communicacion Optica, Universidad Autonoma de San Luis Potosi 78000, San Luis Potosi, SLP, Mexico.
Enciso
Agustin
A