Graph theory plays several important roles in the theory of cellular automata, one of which consists in describing the evolution of the automaton, and another of which consists in relating local properties to global properties. Evolution is described by local rules mapping cell neighborhoods into its subsequent state; because successive neighborhoods overlap it is important to be able to take the overlap into account when relating the behavior of successive cells to one another. In illustration, the de Bruijn diagram and its subdiagrams are applied to the study of cellular automata in one dimension. 1 Introduction An automaton has states and mappings between its states. The concept arose from electrical switching theory, but thanks to the pioneering work of Claude Shannon #1#, boolean algebra and probability theory were seen to haveanimportant role in the theory of switching networks. Speculation concerning the relationship between logical processes and the physiology of the nervous s...

CWI is a founding member of ERCIM, the European Research Consortium for Informatics and Mathematics. CWI's research has a theme-oriented structure and is grouped into four clusters. Listed below are the names of the clusters and in parentheses their acronyms.