Reversible debuggers help programmers to find the causes of misbehaviours in concurrent programs more quickly, by executing a program backwards from the point where a misbehaviour was observed, and looking for the bug(s) that caused it. Reversible debuggers can be founded on the well-studied theory of causal-consistent reversibility, which only allows one to undo an action provided that its consequences, if any, are undone beforehand. Causal-consistent reversibility yields more efficient debugging by reducing the number of states to be explored when looking backwards. Till now, causal-consistent reversibility has never considered time, which is a key aspect in real-world applications. Here, we study the interplay between reversibility and time in concurrent systems via a process algebra. The Temporal Process Language (TPL) by Hennessy and Regan is a well-understood extension of CCS with discrete-time and a timeout operator. We define revTPL, a reversible extension of TPL, and we show that it satisfies the properties expected from a causal-consistent reversible calculus. We show that, alternatively, revTPL can be interpreted as an extension of reversible CCS with time.

翻译：可逆调试器通过从观察到异常行为的点开始反向执行程序，并查找导致该问题的错误，帮助程序员更快地定位并发程序中的异常原因。可逆调试器可基于已得到充分研究的因果一致性可逆理论，该理论仅允许撤销某动作的前提是其后果（如有）已被提前撤销。因果一致性可逆通过减少回溯时的状态探索数量，实现了更高效的调试。迄今为止，因果一致性可逆理论尚未考虑时间因素，而时间在现实应用中是一个关键维度。本文通过进程代数研究并发系统中可逆性与时间的相互作用。Hennessy与Regan提出的时间进程语言（TPL）是带离散时间和超时操作符的CCS扩展，已得到充分理解。我们定义了TPL的可逆扩展revTPL，并证明其满足因果一致性可逆演算的预期性质。进一步地，我们表明revTPL亦可被解释为带时间的可逆CCS扩展。