Reachability of Hennessy–Milner properties for weakly extended PRS

We examine the problem whether a given weakly extended process rewrite system (wPRS) contains a reachable state satisfying a given formula of Hennessy–Milner logic. We show that this problem is decidable. As a corollary we observe that the problem of strong bisimilarity between wPRS and finite-state systems is decidable. Decidability of the same problem for wPRS subclasses, namely PAN and PRS, has been formulated as an open question, see e.g. [Srb02]. We also strengthen some related undecidability results on some PRS subclasses