Cellular Graph Automata. I. Basic Concepts, Graph Property Measurement, Closure Properties

This paper deals with a class of generalized cellular automata in which the intercell connections define a graph of bounded degree. It discusses how such an automaton can measure various properties of its underlying graph, including the radius (as measured from a given node) and the number of nodes, in time proportional to the diameter. Some slower algorithms for measuring the true radius (= the least radius for any node), and for finding bridges and cutnodes, are also discussed. Cellular d -graph languages are shown to be closed under set-theoretic operations, including finite union and intersection; and under “geometric” operations, including permutation of arc end numbering, concatenation, closure, and formation of line graphs. Determinism is preserved under the set-theoretic operations; but under the geometric operations, determinism is known to be preserved only when the languages are also predicates.