Causality serves as an abstract notion of time for concurrent systems. A computation is causal, or simply valid, if each observation of a computation event is preceded by the observation of its causes. The present work establishes that this simple requirement is equally relevant when the occurrence of an event is invertible. We propose a conservative extension of causal models for concurrency that accommodates reversible computations. We first model reversible computations using a symmetric residuation operation in the general model of configuration structures. We show that stable configuration structures, which correspond to prime algebraic domains, remain stable under the action of this residuation. We then derive a semantics of reversible computations for prime event structures, which is shown to coincide with a switch operation that dualizes conflict and causality.

翻译：因果关系为并发系统提供了时间的抽象概念。若计算事件每次被观测前，其因果事件均已被观测，则该计算具有因果性（或称有效性）。本研究证明这一基本要求对可逆事件的发生同样适用。我们提出一种容纳可逆计算的并发因果模型的保守扩展。首先，我们利用配置结构通用模型中的对称剩余运算对可逆计算进行建模。研究表明，对应于素代数域的稳定配置结构在此剩余运算作用下仍保持稳定性。随后，我们推导出素事件结构中可逆计算的语义，该语义被证明与一种将冲突关系与因果关系对偶化的切换操作相一致。