Fixpoint logics on hierarchical structures

Abstract. Hierarchical graph definitions allow a modular description of graphsusing modules for the specification of repeated substructures. Beside this modularity, hierarchical graph definitions allow to specify graphs of exponential sizeusing polynomial size descriptions. In many cases, this succinctness increases the computational complexity of decision problems. In this paper, the model-checking problem for the modal u-calculus and (monadic) least fixpoint logicon hierarchically defined graphs is investigated. In order to analyze the modal u-calculus, parity games on hierarchically defined graphs are studied