Online Monitoring $\omega$-Regular Properties in Unknown Markov Chains

We study runtime monitoring of ω-regular properties. We consider a simple setting in which a run of an unknown finite-state Markov chainM is monitored against a fixed but arbitrary ω-regular specification φ. The purpose of monitoring is to keep aborting runs that are “unlikely” to satisfy the specification untilM executes a correct run. We design controllers for the reset action that (assuming that φ has positive probability) satisfy the following property w.p.1: the number of resets is finite, and the run executed by M after the last reset satisfies φ.

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