We develop a behavioural theory for monitors, computational entities that passively analyse the runtime behaviour of systems so as to infer properties about them. First, we present a monitor language and an instrumentation relation used for piCalculus process monitoring. We then identify contextual behavioural preorders that allow us to relate monitors according to criteria defined over monitored executions of piCalculus processes. Subsequently, we develop alternative monitor preorders that are compositional, since they allow us to relate monitors without resorting to their composite behaviour when they instrumented with systems. Importantly, we show that the latter alternative preorders are sound and complete with respect to the contextual preorders. Finally, we demonstrate how these preorders can assist the development of correct monitor synthesis tools.

我们为监视器开发了行为理论，被动分析系统的运行时行为以推断有关它们的属性的计算实体。首先，我们介绍了用于 piCalculus 进程监控的监控语言和检测关系。然后，我们确定上下文行为预排序，使我们能够根据在 piCalculus 进程的受监控执行上定义的标准关联监视器。随后，我们开发了可组合的替代监视器预订单，因为它们允许我们在监视器与系统进行检测时无需诉诸其复合行为来关联监视器。重要的是，我们证明了后者的替代预序相对于上下文预序是合理和完整的。最后，我们展示了这些预购如何帮助开发正确的监听综合工具。