Bridging Causal Reversibility and Time Reversibility: A Stochastic Process Algebraic Approach

Causal reversibility blends causality and reversibility for concurrent systems. It indicates that an action can be undone provided that all of its consequences have been undone already, thus making it possible to bring the system back to a past consistent state. Time reversibility is instead considered in the field of stochastic processes, mostly for efficient analysis purposes. A performance model based on a continuous-time Markov chain is time reversible if its stochastic behavior remains the same when the direction of time is reversed. We bridge these two theories of reversibility by showing the conditions under which causal reversibility and time reversibility are both ensured by construction. This is done in the setting of a stochastic process calculus, which is then equipped with a variant of stochastic bisimilarity accounting for both forward and backward directions. We also investigate the different compositionality properties and axiomatizations of forward bisimilarity, backward bisimilarity, and forward-backward bisimilarity.