Model checking on trees with path equivalences

For specifying and verifying branching-time requirements, a reactive system is traditionally modeled as a labeled tree, where a path in the tree encodes a possible execution of the system. We propose to enrich such tree models with “jump-edges” that capture observational indistinguishability: for an agent a, an a-labeled edge is added between two nodes if the observable behaviors of the agent a along the paths to these nodes are identical. We show that it is possible to specify information flow properties and partial information games in temporal logics interpreted on this enriched structure. We study complexity and decidability of the model checking problem for these logics. We show that it is PSPACE-complete and EXPTIME-complete respectively for fragments of CTL and μ-calculus-like logics. These fragments are expressive enough to allow specifications of information flow properties such as “agent A does not reveal x (a secret) until agent B reveals y (a password)” and of partial information games.