Evolutionary algorithms for designing reversible cellular automata

Abstract Reversible Cellular Automata (RCA) are a particular kind of shift-invariant transformations characterized by dynamics composed only disjoint cycles. They have many applications in the simulation physical systems, cryptography, and reversible computing. In this work, we formulate search specific class RCA – namely, those whose local update rules defined conserved landscapes as an optimization problem to be tackled with Genetic Algorithms (GA) Programming (GP). particular, our experimental investigation revolves around three different research questions, which address through single-objective, multi-objective, lexicographic approach. single-objective approach, observe that GP can already find optimal solution initial population. This indicates evolutionary algorithms not needed when evolving reversibility such CA, more efficient method is generate at random syntactic trees define rule. On other hand, GA proved quite effective multi-objective approach (1) discover trade-off between Hamming weight landscape rules, (2) CA cannot used symmetric cryptography because their (and thus nonlinearity) too low.