Inf-datalog, Modal Logic and Complexities

E. Foustoucos (1) , Irene Guessarian (2)

1 Department of Mathematics [Athens]
2 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications

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 [\cit{gfaa}]. 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 (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 $\mu$-calcu\-lus, and 2. linear-space (data and program) complexities, linear-time program complexity and polynomial-time data complexity for $L\mu_k$ (modal $\mu$-calculus with fixed alter\-nation-depth at most $k$).

Mots clés: databases; model-checking; specification languages; performance evaluation

Domaines: Algorithme et structure de données [cs.DS]

E. Foustoucos, Irene Guessarian. Inf-datalog, Modal Logic and Complexities. 2007. ⟨hal-00159130⟩