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：因果可逆性将可逆性与因果性融合于并发系统中，它表明仅当某一动作的所有后果已被撤销时，该动作方可被撤销，从而使得系统能够恢复至过去的一致状态。而时间可逆性则主要是在随机过程领域中被研究，通常用于高效分析的目的。若一个基于连续时间马尔可夫链的性能模型在时间方向反转后其随机行为保持不变，则该模型是时间可逆的。我们通过揭示因果可逆性与时间可逆性在何种条件下能够通过构造得以共同保障，从而桥接了这两种可逆性理论。这一研究是在随机过程演算的框架下完成的，该演算随后配备了一种同时兼顾正向与反向方向的随机双模拟关系变体。