Direction-Reversible Self-Timed Cellular Automata for Delay-Insensitive Circuits

We introduce a new Self-Timed Cellular Automaton capable of simulating reversible delay-insensitive (DI) circuits. In addition to a number of reversibility and determinism properties, our STCA exhibits direction-reversibility, where reversing the direction of a signal and running a circuit forwards is equivalent to running the circuit in reverse. We define also several extensions of the STCA which allow us to realise three larger classes of DI circuits, including parallel circuits. We then show which of the reversibility, determinism and direction-reversibility properties hold for these classes of circuits.