Selective Monitoring

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.