We study complexity of the evaluation of fixpoint boundedvariable queries in relational databases. We exhibit a finite database such that the problem whether a closed fixpoint formula using only 2 individual variables is satisfied in this database is PSPACE-complete. This clarifies the issues raised by Moshe Vardi in [Var95]. We study also the complexity of query evaluation for a number of restrictions of fixpoint logic. In particular we exhibit a sublogic for which the upper bound postulated by Vardi holds.

Modal and temporal logics. The most commonly used specification logics in the theory of computer aided verification are based on propositional modal logic augmented by temporal operators. Among those one can broadly distinguish between linear and branching time logics, depending