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 present an extension of the model checker Uppaal, capable of synthesizing linear parameter constraints for the correctness of parametric timed automata. A symbolic representation of the (parametric) state space in terms of parametric difference bound matrices is shown to be correct. A second contribution of this paper is the identification of a subclass of parametric timed automata (L/U automata), for which the emptiness problem is decidable, contrary to the full class where it is known to be undecidable. Also, we present a number of results that reduce the verification effort for L/U automata in certain cases. We illustrate our approach by deriving linear parameter constraints for a number of well-known case studies from the literature (exhibiting a flaw in a published paper).

In this paper, we propose a first efficient on-the-fly algorithm for solving games based on timed game automata with respect to reachability and safety properties. The algorithm we propose is a symbolic extension of the on-the-fly algorithm suggested by Liu & Smolka [15] for linear-time model-checking of finite-state systems. Being on-the-fly, the symbolic algorithm may terminate long before having explored the entire state-space. Also the individual steps of the algorithm are carried out efficiently by the use of so-called zones as the underlying data structure. Various optimizations of the basic symbolic algorithm are proposed as well as methods for obtaining time-optimal winning strategies (for reachability games). Extensive evaluation of an experimental implementation of the algorithm yields very encouraging performance results.

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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".

In this paper we present a framework integrating specification and scheduler generation for real-time systems. In a first step, the system, which can include arbitrarily designed tasks (cyclic or sporadic, with or without precedence constraints, any number of resources and CPUs) is specified as a timed Petri-net. In a second step, our tool generates the most general nonpreemptive online scheduler for the specification, using a controller synthesis technique. 1 Introduction A complex real-time system is typically composed of several tasks that interact. The execution of each task is subject to different kinds of constraints, some of which are proper to the task such as completion times, deadlines and periods, while others, such as resource sharing and synchronization delays, are imposed by the environment in which the tasks are executed. An important problem that arises is the one of ensuring that the tasks can be executed in such a way that (1) they respect the constraints they are su...

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Enormous progress has been achieved in the last decade in the verification of timed systems, making it possible to verify significant real-world protocols. An open challenge is the identification of fully symbolic verification techniques, able to deal effectively with the finite state component as well as with the timing aspects. In this

Abstract. We consider the problem of automatically verifying realtime systems with continuously distributed random delays. We generalise probabilistic timed automata introduced in [19], an extension of the timed automata model of [4], with clock resets made according to continuous probability distributions. Thus, our model exhibits nondeterministic and probabilistic choice, the latter being made according to both discrete and continuous probability distributions. To facilitate algorithmic verification, we modify the standard region graph construction by subdividing the unit intervals in order to approximate the probability to within an interval. We then develop a model checking method for continuous probabilistic timed automata, taking as our specification language Probabilistic Timed Computation Tree Logic (PTCTL). Our method improves on the previously known techniques in that it allows the verification of quantitative probability bounds, as opposed to qualitative properties which can only refer to bounds of probability 0 or 1. 1

In this paper we show how the classical job-shop scheduling problem can be modeled as a special class of acyclic timed automata. Finding an optimal schedule corresponds, then, to nding a shortest (in terms of elapsed time) path in the timed automaton. This representation provides new techniques for solving the optimization problem and, more importantly, it allows to model naturally more complex dynamic resource allocation problems which are not captured so easily in traditional models of operation research. We present several algorithms and heuristics for nding the shortest paths in timed automata and test their implementation in the tool Kronos on numerous benchmark examples.