Asynchronous ballistic reversible computing

Most existing concepts for hardware implementation of reversible computing invoke an adiabatic computing paradigm, in which individual degrees of freedom (e.g., node voltages) are synchronously transformed under the influence of externally- supplied driving signals. But distributing these "power/clock" signals to all gates within a design while efficiently recovering their energy is difficult. Can we reduce clocking overhead using a ballistic approach, wherein data signals self- propagating between devices drive most state transitions? Traditional concepts of ballistic computing, such as the classic Billiard-Ball Model, typically rely on a precise synchronization of interacting signals, which can fail due to exponential amplification of timing differences when signals interact. In this paper, we develop a general model of Asynchronous Ballistic Reversible Computing (ABRC) that aims to address these problems by eliminating the requirement for precise synchronization between signals. Asynchronous reversible devices in this model are isomorphic to a restricted set of Mealy finite- state machines. We explore ABRC devices having up to 3 bidirectional I/O terminals and up to 2 internal states, identifying a simple pair of such devices that comprises a computationally universal set of primitives. We also briefly discuss how ABRC might be implemented using single flux quanta in superconducting circuits.