On the average-case complexity of the reversibility problem for finite cellular automata

Abstract

Of particular relevance in the theory and applications of cellular automata is the concept of invertibility. We study the computational complexity of deciding whether or not a given finite cellular automata is invertible. This problem is known to be CoNP-complete, we prove that the expected-time complexity of its randomized version is hard: the problem is CoRNP-complete. Finally, we discuss some consequences of this result in the theory and applications of cellular automata. >