The Modal μ-Calculus Hierarchy on Restricted Classes of Transition Systems.

Luca Alberucci (1) , Alessandro Facchini (2)

1 IAM - Institute of Computer Science and Applied Mathematics
2 LaBRI - Laboratoire Bordelais de Recherche en Informatique

We discuss the strictness of the modal µ-calculus hierarchy over some restricted classes of transition systems. First, we show that the hierarchy is strict over reflexive frames. By proving the finite model theorem for reflexive systems the same results holds for finite models. Second, we prove that over transitive systems the hierarchy collapses to the alternation-free fragment. In order to do this the finite model theorem for transitive transition systems is also proved. Further, we verify that if symmetry is added to transitivity the hierarchy collapses to the purely modal fragment.

Domaines: Logique en informatique [cs.LO]; Logique [math.LO]

Luca Alberucci, Alessandro Facchini. The Modal μ-Calculus Hierarchy on Restricted Classes of Transition Systems.. The Journal of Symbolic Logic, 2009, 74 (4), pp.1367-1400. ⟨hal-00396431⟩