A Criterion for Stability in Random Boolean Cellular Automata

Abstract

Random boolean cellular automata are investigated, where each gate has two randomly chosen inputs and is randomly assigned a boolean function of its inputs. The effect of non-uniform distributions on the choice of the boolean functions is considered. The main results are that if the gates are more likely to be assigned constant functions than non-canalyzing functions, then with very high probability, the automaton will exhibit very stable behavior: most of the gates will stabilize, and the state cycles will be bounded in size.