Specifying budgets and deadlines using a process algebra like CSP requires an explicit notion of time. The tock-CSP encoding embeds a rich and flexible approach for modelling discrete-time behaviours with powerful tool support. It uses an event tock, interpreted to mark passage of time. Analysis, however, has traditionally used the standard semantics of CSP, which is inadequate for reasoning about timed refinement. The most recent version of the model checker FDR provides tailored support for tock-CSP, including specific operators, but the standard semantics remains inadequate. In this paper, we characterise tock-CSP as a language in its own right, rich enough to model budgets and deadlines, and reason about Zeno behaviour. We present the first sound tailored semantic model for tock-CSP that captures timewise refinement. It is fully mechanised in Isabelle/HOL and, to enable use of FDR4 to check refinement in this novel model, we use model shifting, which is a technique that explicitly encodes refusals in traces.

使用像CSP这样的过程代数来指定预算和最后期限需要一个明确的时间概念。该滴答-csp编码嵌入与功能强大的工具支持建模离散时间行为，丰富和灵活的方法。它使用事件tock解释为标记时间的流逝。但是，分析传统上使用CSP的标准语义，这不足以进行时间精炼的推理。模型检查器FDR的最新版本为tock -CSP提供了量身定制的支持，包括特定的运算符，但是标准语义仍然不足。在本文中，我们表征了托克-CSP本身就是一种语言，其功能足以建模预算和截止日期，并提供有关芝诺（​​Zeno）行为的理由。我们介绍了第一个针对tock -CSP的声音定制语义模型，该模型捕获了时间上的细化。它在Isabelle / HOL中完全机械化，并且为了能够使用FDR4来检查此新颖模型中的细化程度，我们使用模型移位，该技术可对轨迹中的拒绝进行明确编码。