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

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

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 pu...

The μ-calculus alternation hierarchy collapses over structures with restricted connectivity

It is known that the alternation hierarchy of least and greatest fixpoint operators in the μ-calculus is strict. However, the strictness of the alternation hierarchy does not necessarily carry over when considering restricted classes of structures. A prominent instance is the class of infinite words over which the alternation-free fragment is already as expressive as the full μ-calculus. Our cu...

The \mu-Calculus Alternation Hierarchy Collapses over Structures with Restricted Connectivity

It is known that the alternation hierarchy of least and greatest fixpoint operators in the μ-calculus is strict. However, the strictness of the alternation hierarchy does not necessarily carry over when considering restricted classes of structures. A prominent instance is the class of infinite words over which the alternation-free fragment is already as expressive as the full μ-calculus. Our cu...

A Modal µ-Calculus for Durational Transition Systems

On Hybrid Systems and the Modal µ-calculus

We start from a basic and fruitful idea in current work on the formal analysis and veriication of hybrid and real-time systems: the uniform representation of both sorts of state dynamics { both continuous evolution within a control mode, and the eeect of discrete jumps between control modes { as abstract transition relations over a hybrid space X Q R n , where Q is a nite set of control modes. ...