Reversible space–time simulation of cellular automata
Résumé
The goal of this paper is to design a reversible $d$-dimensional cellular automaton which is capable of simulating the behavior of any given $d$-dimensional cellular automaton over any given configuration (even infinite) with respect to a well suited notion of simulation we introduce. We generalize a problem which was originally addressed in a paper by Toffoli in $1977$. He asked whether a $d$-dimensional reversible cellular automaton could simulate $d$-dimensional cellular automata. In the same paper he proved that there exists a $d{+}1$-dimensional reversible cellular automaton which can simulate a given $d$-dimensional cellular automaton. To prove our result, we use as an intermediate model partition cellular automata defined by Morita et al. in 1989.