Stochastic Games for Verification of Probabilistic Timed Automata

Abstract

Abstract. Probabilistic timed automata (PTAs) are used for formal modelling and verification of systems with probabilistic, nondeterministic and real-time behaviour. For non-probabilistic timed automata, forwards reachability is the analysis method of choice, since it can be implemented extremely efficiently. However, for PTAs, such techniques are only able to compute upper bounds on maximum reachability probabilities. In this paper, we propose a new approach to the analysis of PTAs using abstraction and stochastic games. We show how efficient forwards reachability techniques can be extended to yield both lower and upper bounds on maximum (and minimum) reachability probabilities. We also present abstraction-refinement techniques that are guaranteed to improve the precision of these probability bounds, providing a fully automatic method for computing the exact values. We have implemented these techniques and applied them to a set of large case studies. We show that, in comparison to alternative approaches to verifying PTAs, such as backwards reachability and digital clocks, our techniques exhibit superior performance and scalability.

Advances in Quantitative Verification for Ubiquitous Computing

“…PTAs naturally model distributed randomised algorithms with timing, for example the ZeroConf protocol, as well as the medium access protocols for wireless networks, including WiFi, Bluetooth and ZigBee; all have been analysed with PRISM [1]. A number of techniques have been developed for quantitative verification of PTAs, including the digital clocks [36] approach; forwards [37] and backwards reachability [38] based on zones; and game-based quantitative abstraction-refinement [33]. Strategy synthesis is also possible [44].…”

“…Strategy synthesis is also possible [44]. PRISM provides native support for PTAs, via the techniques of [33] and [36].…”

Practical Applications of Probabilistic Model Checking to Communication Protocols

“…In [25] such an approach, based on a forwards traversal of the state space, is introduced. Subsequent work in [22] extends its applicability through the use of abstraction refinement and stochastic games. On the other hand, the techniques developed in [28] are based on a backwards exploration of the state space and have since been applied to the analysis of cost and reward properties [5,12].…”

Advances in Probabilistic Model Checking

“…• probabilistic real-time systems, modelled using probabilistic timed automata [54] (see the next section for a more in-depth discussion); • probabilistic software, based on the use of ANSI-C code, augmented with probabilistic commands [46]; • concurrent probabilistic programs, as analysed by the probabilistic abstraction tool PASS [29]; • probabilistic programs over arbitrary abstract domains [27];…”