Model Checking the Quantitative mu-Calculus on Linear Hybrid Systems

We study the model-checking problem for a quantitative extension of the modal mu-calculus on a class of hybrid systems. Qualitative model checking has been proved decidable and implemented for several classes of systems, but this is not the case for quantitative questions that arise naturally in this context. Recently, quantitative formalisms that subsume classical temporal logics and allow the measurement of interesting quantitative phenomena were introduced. We show how a powerful quantitative logic, the quantitative mu-calculus, can be model checked with arbitrary precision on initialised linear hybrid systems. To this end, we develop new techniques for the discretisation of continuous state spaces based on a special class of strategies in model-checking games and present a reduction to a class of counter parity games.Comment: LMCS submissio

STORMED hybrid systems

Abstract. We introduce STORMED hybrid systems, a decidable class which is similar to o-minimal hybrid automata in that the continuous dynamics and constraints are described in an o-minimal theory. However, unlike o-minimal hybrid automata, the variables are not initialized in a memoryless fashion at discrete steps. STORMED hybrid systems require flows which are monotonic with respect to some vector in the continuous space and can be characterised as bounded-horizon systems in terms of their discrete transitions. We demonstrate that such systems admit a finite bisimulation, which can be effectively constructed provided the o-minimal theory used to describe the system is decidable. As a consequence, many verification problems for such systems have effective decision algorithms