We study selective monitors for labelled Markov chains. Monitors observe the outputs that are generated by a Markov chain during its run, with the goal of identifying runs as correct or faulty. A monitor is selective if it skips observations in order to reduce monitoring overhead. We are interested in monitors that minimize the expected number of observations. We establish an undecidability result for selectively monitoring general Markov chains. On the other hand, we show for non-hidden Markov chains (where any output identifies the state the Markov chain is in) that simple optimal monitors exist and can be computed efficiently, based on DFA language equivalence. These monitors do not depend on the precise transition probabilities in the Markov chain. We report on experiments where we compute these monitors for several open-source Java projects.

我们研究标记的马尔可夫链的选择性监测器。监控器观察马尔可夫链在运行过程中生成的输出，目的是将运行识别为正确或错误。如果监视器跳过一些观测以减少监视开销，则它是选择性的。我们对最小化预期观察数的监测器感兴趣。我们建立了不确定性结果，可以选择性地监视一般的马尔可夫链。另一方面，我们针对非隐藏的马尔可夫链（其中任何输出标识了马尔可夫链所处的状态）表明，存在简单的最佳监控器，并且可以基于DFA语言等效性进行有效地计算。这些监视器不依赖于马尔可夫链中的精确过渡概率。我们报告有关为几个开源Java项目计算这些监视器的实验。