Reversible cellular automata

Abstract

A reversible cellular automaton (RCA) is a special type of cellular automaton (CA) such that every configuration of it has only one previous configuration, and hence its evolution process can be traced backward uniquely. Here, we discuss how RCAs are defined, their properties, how one can find and design them, and their computing abilities. After describing definitions on RCAs, a survey is given on basic properties on injectivity and surjectivity of their global functions. Three design methods of RCAs are then given: using CAs with block rules, partitioned CAs, and second-order CAs. Next, the computing ability of RCAs is discussed. In particular, we present simulation methods for irreversible CAs, reversible Turing machines, and some other universal systems by RCAs, in order to clarify the universality of RCAs. In spite of the strong constraint of reversibility, it can be seen that RCAs have rich abilities in computing and information processing, and even very simple RCAs have universal computing ability.