Number-Conserving Reversible Cellular Automata and Their Computation-Universality

¹ Hiroshima University, Faculty of Engineering, Higashi-Hiroshima 739-8527, Japan; e-mail: morita@iec.hiroshima-u.ac.jp
² Hiroshima University, Faculty of Engineering, Higashi-Hiroshima 739-8527, Japan; e-mail: imai@iec.hiroshima-u.ac.jp

Received: 27 August 1999
Accepted: 21 August 2001

Abstract

We introduce a new model of cellular automaton called a one-dimensional number-conserving partitioned cellular automaton (NC-PCA). An NC-PCA is a system such that a state of a cell is represented by a triple of non-negative integers, and the total (i.e., sum) of integers over the configuration is conserved throughout its evolving (computing) process. It can be thought as a kind of modelization of the physical conservation law of mass (particles) or energy. We also define a reversible version of NC-PCA, and prove that a reversible NC-PCA is computation-universal. It is proved by showing that a reversible two-counter machine, which has been known to be universal, can be simulated by a reversible NC-PCA.