The modal μ-calculus hierarchy over restricted classes of transition systems
L. Alberucci and A. Facchini
Source: J. Symbolic Logic Volume 74, Issue 4 (2009), 1367-1400.
Abstract
We study the strictness of the modal μ-calculus hierarchy over some restricted classes of transition systems. First, 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 proved. Further, we verify that if symmetry is added to transitivity the hierarchy collapses to the purely modal fragment. Finally, 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.
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Permanent link to this document: http://projecteuclid.org/euclid.jsl/1254748696
Digital Object Identifier: doi:10.2178/jsl/1254748696
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