In the past, action-based, process-algebraic formalisms for the description and analysis of concurrent reversible computations were mainly developed. In this paper, we present a state-based approach to the specification of concurrent systems in which forward-executed actions may either be executed in reverse in a causal-consistent uncontrolled fashion or are irreversible. The basic underlying system semantics is assumed to be a set of possible infinite sequences of states with actions defined as state transitions, which allows us to specify reversibility with the specification language TLA⁺ and to use its tool support for specification editing and verification. We provide definitions of TLA⁺ operators for the specification of causal-consistent reversibility and irreversible actions in a uniform way. The reversibility is achieved by remembering as much computation history as necessary with regard to the irreversible actions. The applicability of the approach is illustrated with examples, including the modelling of the influence of the Raf kinase inhibitor protein on the extracellular signal-regulated kinase signalling pathway and parameterised specification of a system of dining philosophers.

过去，主要开发用于描述和分析并行可逆计算的基于动作，过程代数的形式主义。在本文中，我们提出了一种基于状态的并发系统规范方法，其中前向执行的动作可能以因果一致的不受控制的方式反向执行，或者是不可逆的。假定基本的基本系统语义是一组可能的无限状态序列，并且将动作定义为状态转换，这使我们能够指定规范语言TLA ^+的可逆性，并使用其工具支持进行规范编辑和验证。我们提供TLA ^+的定义因果一致的可逆性和不可逆动作的规范操作符。通过记住关于不可逆动作的尽可能多的计算历史来实现可逆性。通过实例说明了该方法的适用性，包括对Raf激酶抑制剂蛋白对细胞外信号调节激酶信号通路的影响进行建模，以及就餐哲学家系统的参数化规范。