Inf-datalog, Modal Logic and Complexities

Inf-Datalog extends the usual least fixpoint semantics of Datalog with greatest fixpoint semantics: we defined inf-Datalog and characterized the expressive power of various fragments of inf-Datalog in [CITE]. In the present paper, we study the complexity of query evaluation on finite models for (various fragments of) inf-Datalog. We deduce a unified and elementary proof that global model-checking (i.e. computing all nodes satisfying a formula in a given structure) has 1. quadratic data complexity in time and linear program complexity in space for CTL and alternation-free modal μ-calculus, and 2. linear-space (data and program) complexities, linear-time program complexity and polynomial-time data complexity for Lµk (modal μ-calculus with fixed alternation-depth at most k).