Automatic Verification of Real-Time Systems with Discrete Probability Distributions

Abstract

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".

Stochastic Hybrid Systems: Application to Communication Networks

“…Probabilistic Automata [15,27,34,44,48] also provided motivation for our work, which builds upon them as deterministic hybrid systems build upon deterministic automata.…”

Stochastic Games for Verification of Probabilistic Timed Automata

“…We can easily consider more expressive targets, that refer to both locations and clock values, through a simple syntactic modification of the PTA [16].…”

“…Probabilistic timed automata (PTAs) [9,1,16], which are finite state automata extended with real-valued clocks and discrete probabilistic choice, are a natural formalism for modelling and analysing such systems. Formal verification techniques for PTAs can help to identify anomalies resulting from the subtle interplay between probabilistic, real-time and nondeterministic aspects of these systems.…”

“…There are three main existing algorithmic approaches to the verification of PTAs: (i) forwards reachability [16,5]; (ii) backwards reachability [17]; and (iii) digital clocks [15]. Forwards reachability is based on a symbolic forwards exploration, similar to the techniques implemented in state-of-the art tools for nonprobabilistic timed automata [6,18].…”

“…We first show how the forwards reachability technique of [16] can be generalised to produce a stochastic game that yields lower and upper bounds on either minimum or maximum reachability probabilities of PTAs. Then, using abstraction-refinement methods, we show how the stochastic game can be iteratively refined in order to tighten these bounds.…”