Linear Time Algorithm for Identifying the Invertibility of Null-Boundary Three Neighborhood Cellular Automata

This paper reports an algorithm to check for the invertibility of null-boundary three neighborhood cellular automata (CAs). While the best known result for checking invertibility is quadratic [1, 2], the complexity of the proposed algorithm is linear. An efficient data structure called a rule vector graph (RVG) is proposed to represent the global functionality of a cellular automaton (CA) by its rule vector (RV). The RVG of a null-boundary invertible CA preserves the specific characteristics that can be checked in linear time. These results are shown in the more general case of hybrid CAs. This paper also lists the elementary rules [3] that are invertible.