Formal Methods in System Design Monitorability for the Hennessy-Milner Logic with Recursion

We study muHML, a branching-time logic with least and greatest fix-points, 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. We define a monitorsynthesis algorithm for this subset and then show that the synthesised monitors correctly perform the required analysis from the observed behaviour. We also prove completeness results with respect to 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. Powered by Editorial Manager® and ProduXion Manager® from Aries Systems Corporation Noname manuscript No. (will be inserted by the editor) Monitorability for the Hennessy-Milner Logic with