O N O-aut Omata

Abst ract . A c -a utomaton is a part icularl y sim ple type of cellu la r automaton on a grap h; each cell is either in stale 0 or 1 and the next sta te of a cell is determined by addi ng the sta tes of it s neighbors modulo two . Using algebraic an d gra ph-theoretic techniques, questions such as reversibility and existe nce of predecessor configura tions of th ese automata will be st udied . \Ve deri ve some gene ral result s for prod uct graphs. In particular, we give a simple characterization of th e numb er of predecessors of a configuration in rect angular grids, cylinders, a nd tori .