Computation-universality of one-dimensional one-way reversible cellular automata

Abstract

A reversible (or injective) cellular automaton (RCA) is a “backward deterministic” CA, i.e., every configuration of it has at most one predecessor. Reversible systems have been studied to investigate the limitation of inevitable power dissipation in computing processes, and many interesting results have been shown (see e.g. [2-41X As for RCA, Toffoli [9] showed that every (irreversible) k-dimensional CA can be simulated by a k + l-dimensional RCA and thus two-dimensional RCA is computation-universal. In the two-dimensional case, Margolus [5] gave a very simple computation-universal model of 2-state RCA with so-called Margolus neighborhood. On the other hand, Morita and Ueno [8] showed two universal models of two-dimensional 16-state RCA with usual von Neumann neighborhood. In the one-dimensional case, it has been shown by Morita and Harao [6] that a three-neighbor RCA is computation-universal. In this paper, we investigate the computing ability of a one-dimensional two-neighbor (i.e., one-way) RCA. We first investigate a one-dimensional partitioned cellular automaton (PCA), a special subclass of a CA, and show that a three-neighbor RPCA can be simu-