Compositional Visible Bisimulation Abstraction Applied to Opacity Verification ⁎⁎This work was carried out within the project SyTec - Systematic Testing of Cyber-Physical Systems, a Swedish Science Foundation grant for strong research environment. The support is gratefully acknowledged.
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In this paper, an alternative equivalence based definition of bisimulation is proposed, called visible bisimulation equivalence. It includes both state and transition labels and therefore unifies stuttering and branching bisimulation. Furthermore, it is equivalent to a temporal logic called ECTL*, where CTL* is extended with events. The presented bisimulation abstraction is applied to a set of synchronized submodels, where local events are identified incrementally and abstracted after each synchronization. Since the bisimulation reduction is applied after each synchronization, a significant part of the state space explosion in ordinary synchronization is avoided. This compositional abstraction is used for opacity verification, where it is shown that local observers can be generated before they are synchronized, a key factor to be able to apply compositional opacity verification. The efficiency of this method is illustrated on a modular opacity problem with mutual exclusion of moving agents.