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关系融合于并发系统中。它表明，一个动作只有在所有后果均已被撤销后方可撤销，从而使系统能够恢复到过去的一致状态。时间可逆性则主要在随机过程领域中被研究，通常用于高效分析的目的。基于连续时间马尔可夫链的性能模型，若其随机行为在时间方向反转后保持不变，则称其为时间可逆。我们通过展示在何种条件下因果可逆性与时间可逆性均能被确保建构，从而弥合了这两种可逆性理论。这一工作基于随机过程演算的框架，并进一步为该演算配备了同时考虑正向与反向的随机互模拟变体。