On the expressive power of hybrid branchingtime logics Abstract   Hybrid branchingtime logics are a powerful extension of branchingtime logics like CTL, CTLxe2x81x8e or even the modal xcexbccalculus through the addition of binders, jumps and variable tests. Their expressiveness is not restricted by bisimulationinvariance anymore. Hence, they do not retain the tree model property, and the finite model property is equally lost. Their satisfiability problems are typically undecidable, their model checking problems (on finite models) are decidable with complexities ranging from polynomial to nonelementary time.  In this paper we study the expressive power of such hybrid branchingtime logics. We extend the hierarchy of branchingtime logics CTL, CTL, CTLxe2x81x8e and the modal xcexbccalculus to their hybrid extensions. We show that most separation results can be transferred to the hybrid world, even though the required techniques become more involved. We also present collapse results for linear, treeshaped and finite models.

Upto Techniques for Branching Bisimilarity. Ever since the introduction of behavioral equivalences on processes one has been searching for efficient proof techniques that accompany those equivalences. Both strong bisimilarity and weak bisimilarity are accompanied by an arsenal of upto techniques: enhancements of their proof methods. For branching bisimilarity, these results have not been established yet. We show that a powerful proof technique is sound for branching bisimilarity by combining the three techniques of up to union, up to expansion and up to context for Bloomu0027s BB cool format. We then make an initial proposal for casting the correctness proof of the up to context technique in an abstract coalgebraic setting, covering branching but also eta, delay and weak bisimilarity.