Fast One-Way Cellular Automata with Reversible Mealy Cells

Abstract : We investigate cellular automata that are composed of reversible components with regard to the recognition of formal languages. In particular, real-time one-way cellular automata ($\text {OCA}$) are considered which are composed of reversible Mealy automata. Moreover, we differentiate between three notions of reversibility in the Mealy automata, namely, between weak and strong reversibility as well as reversible partitioned $\text {OCA}$ which have been introduced by Morita in [14]. Here, it turns out that every real-time $\text {OCA}$ can be transformed into an equivalent real-time $\text {OCA}$ with weakly reversible automata in its cells, whereas the remaining two notions seem to be weaker. However, a non-semilinear language is provided that can be accepted by a real-time $\text {OCA}$ with strongly reversible cells. On the other hand, we present a context-free, non-regular language that is accepted by some real-time reversible partitioned $\text {OCA}$.