Cellular Automata with Large Cycle Generator

Abstract

This paper presents an efficient mechanism on the design of n-cell reversible cellular automaton which can produce a cycle of a given length k where n is “near optimal”. Here, we develop an operator which allows to design a cellular automaton of size $n_1+n_2$ having length lcm($k_1$, $k_2$) by using two cellular automata of sizes $n_1$ and $n_2$ having cycle lengths $k_1$ and $k_2$ respectively. Our approach is to apply a stochastic method to synthesize cellular automata having large cycles in their configuration spaces, and then apply the operator repeatedly on these cellular automata to design the target automaton. We show that this is an optimization problem, and then apply a novel biologically inspired algorithm to solve the problem.