Monitorability for the Hennessy-Milner logic with recursion

We study μHML, a branching-time logic with least and greatest fixpoints, from a runtime verification perspective. The logic may be used to specify properties of programs whose behaviour may be expressed as a labelled transition system. We establish which subset of this logic can be monitored for at runtime by merely observing the runtime execution of a program. A monitor-synthesis algorithm is defined for this subset, where it is shown that the resulting synthesised monitors correctly perform the required analysis from the observed behaviour. We also prove completeness results wrt. this logical subset that show that, up to logical equivalence, no other properties apart from those identified can be monitored for and verified at runtime.