Model checking real-time properties of symmetric systems

We develop efficient algorithms for model checking quantitative properties of symmetric reactive systems in the general framework of a Real-Time Mu-calculus. Previous work has been limited to qualitative correctness properties. Our work not only permits handling of quantitative correctness, but it provides a strictly more expressive framework for qualitative correctness since the Mu-calculus strictly subsumes, e.g, CTL*. Unlike the previous "group-theoretic" approaches of [CE96] and [ES96] and the technical "automata-theoretic" approach of [ES97], our new approach may be viewed as "model-theoretic".