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.

翻译：显示一项行动可以撤销,只要其所有后果都已撤销,从而有可能使系统恢复到过去的一致性状态。时间的可逆性主要用于高效分析。基于连续时间的Markov链的性能模型如果在时间方向被逆转时其随机性行为保持不变,则具有可逆性。我们通过显示建筑确保因果可逆性和时间可逆性的条件,将这两种可逆性理论连接起来。这是在设计一个随机性过程的计算过程中进行的,然后为前向和后向两个方向配备一个可变式的相异计算。