Graphs Related to Reversibility and Complexity in Cellular Automata

Abstract

Concepts from graph theory have been used in the local and global analysis and characterization of a cellular automaton (CA). In particular, De Bruijn graph, pair graph, subset graph, and cycle graph have been employed to represent the local cell-state transition rules and their induced global transformations. These graphs are useful to analyze, classify, and construct interesting dynamics in one-dimensional CAs. Reversibility and complexity have been a common field of study where graphic tools have been successfully applied.