Selective Monitoring

TL;DR

This paper investigates selective monitoring of labelled Markov chains, establishing undecidability in general but providing efficient solutions for non-hidden chains, with practical experiments on Java projects.

Contribution

It proves undecidability for general Markov chains and offers an efficient method for optimal monitoring in non-hidden chains, independent of transition probabilities.

Findings

Optimal monitors can be computed efficiently for non-hidden Markov chains.

Selective monitors significantly reduce observation overhead.

Experimental results demonstrate practical applicability on Java projects.

Abstract

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.