Reversible computation in asynchronous cellular automata

Reversible computation has attracted much attention over the years, not only for its promise for computers with radically reduced power consumption, but also for its importance for Quantum Computing. Though studied extensively in a great variety of synchronous computation models, it is virtually unexplored in an asynchronous framework. Particularly suitable asynchronous models for the study of reversibility are asynchronous cellular automata. Simple yet powerful, they update their cells at random times that are independent of each other. In this paper, we present the embedding of a universal reversible Turing machine (RTM) in a two-dimensional self-timed cellular automaton (STCA), a special type of asynchronous cellular automaton, of which each cell uses four bits to store its state, and a transition on a cell accesses only these four bits and one bit of each of the four neighboring cells. The embedding of a universal RTM on an STCA requires merely four rotation-symmetric transition rules, which are bit-conserving and locally reversible. We show that the model is globally reversible.