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