Abstract. We consider the timed automata model of [3], which allows the analysis of real-time systems expressed in terms of quantitative timing constraints. Traditional approaches to real-time system description express the model purely in terms of nondeterminism; however, we may wish to express the likelihood of the system making certain transitions. In this paper, we present a model for real-time systems augmented with discrete probability distributions. Furthermore, using the algorithm of [5] with fairness, we develop a model checking method for such models against temporal logic properties which can refer both to timing properties and probabilities, such as, “with probability 0.6 or greater, the clock x remains below 5 until clock y exceeds 2”. 1

We consider probabilistic timed automata of [13], an extension of the timed automata model of [2] with discrete probability distributions. In contrast to timed automata, which model real-time systems purely in terms of nondeterminism, our model allows to express the likelihood of the system making certain transitions, and is thus appropriate for modelling fault-tolerance and probabilistic failures. We present a symbolic model checking algorithm for the existential fragment of the logic PTCTL of [13] based on backward reachability as in [12]. The logic allows us to specify properties such as \with probability 0.99 or greater, it is possible to correctly deliver a data packet within 5 time units", or \with probability 0.87 or greater, the system never enters an error state".

Abstract. The parallel composition with observers is a well-known approach to check or test properties over formal models of concurrent and real-time systems. We present a newtechnique to reduce the size of the resulting model. Our approach has been developed for a formalism based on Timed Automata. Firstly, it discovers relevant components and clocks at each location of the observer using influence information. Secondly, it outcomes an abstraction which is equivalent to the original model up to branching-time structure and can be treated by verification tools such as Kronos [12] or OpenKronos [23]. Our experiments suggest that the approach may lead to significant time and space savings during verification phase due to state space reduction and the existence of shorter counterexamples in the optimized model. 1

In this work we present an Eclipse plug-in for the VInTiMe (Verifier of INtegrated TImed ModEls) 1 suite of tools that combines high-level expressive power, unassisted propertypreserving model reduction and distributed model checking to describe and verify complex real-time system designs and their properties.