Reversible Cellular Automata

Abstract

A cellular automaton (CA) is a discrete model for a spatiotemporal phenomenon. In a CA, an infinite number of cells are placed uniformly in the space, and each cell changes its state depending on its neighboring cells by a local function. Applying the local function to all the cells in parallel, a global function is induced, by which the configuration of the cellular space evolves. A reversible CA (RCA) is one whose global function is injective. It is thus considered as an abstract model of a reversible space.We use RCAs for studying how computation and information processing are performed in a reversible space. If we use the framework of classical CAs, however, it is generally difficult to design RCAs. Instead, we use the framework of partitioned cellular automata (PCAs). Based on it, various RCAs with interesting features and/or computational universality are designed in this and in the following chapters. It is also a useful model to investigate how complex phenomena appear from a very simple reversible local function. In this chapter, after giving basic properties of RCAs, methods of simulating irreversible CAs by reversible ones, and of constructing PCAs from reversible logic elements are shown.