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The modal μ-calculus hierarchy over restricted classes of transition systems

Published online by Cambridge University Press:  12 March 2014

Luca Alberucci  and
Alessandro Facchini
Luca Alberucci
Affiliation:
Institute for Applied Mathematics, University of Bern, Ch-3012 Bern, Switzerland, E-mail: albe@iam.unibe.ch
Alessandro Facchini
Affiliation:
Isi-Hec, University of Lausanne, Ch-1015 Lausanne, Switzerland Labri, University of Bordeaux 1, 351, Cours de la Liberation, F-33405 Talence Cedex, France, E-mail: alessandro.facchini@unil.ch
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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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 74 , Issue 4 , December 2009 , pp. 1367 - 1400
Copyright
Copyright © Association for Symbolic Logic 2009

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