Causal reversibility blends reversibility and causality 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.

翻译：因果可逆性融合了并发系统中的可逆性与因果关系。它表明一个动作可以被撤销，前提是其所有后果已被撤销，从而使得系统能够恢复到过去的一致状态。而时间可逆性则在随机过程领域中主要出于高效分析的目的被考虑。基于连续时间马尔可夫链的性能模型在时间方向反转时，若其随机行为保持不变，则称该模型具有时间可逆性。我们通过展示在何种条件下因果可逆性与时间可逆性能够通过构造同时得到保证，桥接了这两种可逆性理论。这一研究在随机过程演算的框架下完成，并为该演算配备了一种考虑前向与后向两个方向的随机双模拟变体。