Sharp Congruences Adequate with Temporal Logics Combining Weak and Strong Modalities

We showed in a recent paper that, when verifying a modal?-calculus formula, the actions of the system under verification can bepartitioned into sets of so-called weak and strong actions, depending onthe combination of weak and strong modalities occurring in the formula.In a compositional verification setting, where the system consists of pro-cesses executing in parallel, this partition allows us to decide whethereach individual process can be minimized for either divergence-preservingbranching (if the process contains only weak actions) or strong (other-wise) bisimilarity, while preserving the truth value of the formula. In thispaper, we refine this idea by devising a family of bisimilarity relations,named sharp bisimilarities, parameterized by the set of strong actions.We show that these relations have all the nice properties necessary tobe used for compositional verification, in particular congruence and ad-equacy with the logic. We also illustrate their practical utility on severalexamples and case-studies, and report about our success in the RERS2019 model checking challenge.