Fortuna: Model Checking Priced Probabilistic Timed Automata

Abstract. In this paper we consider the problem of computing the minimum expected time to reach a target and the synthesis of the corresponding optimal controller for a probabilistic timed automaton (PTA). Although this problem admits solutions that employ the digital clocks abstraction or statistical model checking, symbolic methods based on zones and priced zones fail due to the difficulty of incorporating probabilistic branching in the context of dense time. We work in a generalisation of the setting introduced by Asarin and Maler for the corresponding problem for timed automata, where simple and nice functions are introduced to ensure finiteness of the dense-time representation. We find restrictions sufficient for value iteration to converge to the minimum expected time on the uncountable Markov decision process representing the semantics of a PTA. We formulate a Bellman operator on the backwards zone graph of a PTA and prove that value iteration using this operator equals that computed over the PTA's semantics. This enables us to extract an ε-optimal controller from value iteration in the standard way.

Section: Resultsmentioning

confidence: 99%

“…Although this problem is shown to be undecidable [6], a semi-decidable backwards algorithm using priced zones, which terminates if the problem is affirmative, is implemented in Fortuna [8].…”

Section: Introductionmentioning

confidence: 99%

Symbolic Minimum Expected Time Controller Synthesis for Probabilistic Timed Automata

Jovanovic

Kwiatkowska

Norman

2015

“…As for digital clocks, a finitestate MDP is then built and model checked to obtain results. Although the operations required to implement this approach can be expensive, with appropriate optimisations [13] it has been shown to perform well.…”

Section: Model Checking For Ptasmentioning

confidence: 99%

“…Other tools providing model checking of MDPs include LiQuor [18] and ProbDiVinE [11]. Software supporting verification of PTAs includes UPPAAL-PRO [66], Fortuna [13] and mcpta [37]. A more detailed list of probabilistic model checking tools can be found at [68].…”

Section: Probabilistic Model Checking In Practicementioning

confidence: 99%

Advances in Probabilistic Model Checking

Katoen

2010

Abstract. Probabilistic model checking is an automated verification method that aims to establish the correctness of probabilistic systems. Probability may arise, for example, due to failures of unreliable components, communication across lossy media, or through the use of randomisation in distributed protocols. Probabilistic model checking enables a range of exhaustive, quantitative analyses of properties such as "the probability of a message being delivered within 5ms is at least 0.89".In the last ten years, probabilistic model checking has been successfully applied to numerous real-world case studies, and is now a highly active field of research. This tutorial gives an introduction to probabilistic model checking, as well as presenting material on selected recent advances. The first half of the tutorial concerns two classical probabilistic models, discrete-time Markov chains and Markov decision processes, explaining the underlying theory and model checking algorithms for the temporal logic PCTL. The second half discusses two advanced topics: quantitative abstraction refinement and model checking for probabilistic timed automata. We also briefly summarise the functionality of the probabilistic model checker PRISM, the leading tool in the area.

“…A second tool supporting PTAs is mcpta [20], which applies the digital clocks abstraction to translate a subset of the modelling language Modest [15] directly into the PRISM modelling language. The related problem of price-bounded probabilistic reachability [10] (known to be undecidable [9]) can be analysed via a semi-decision procedure using priced zones, implemented in Fortuna [11].…”

Section: Introductionmentioning

confidence: 99%

Symbolic Verification and Strategy Synthesis for Linearly-Priced Probabilistic Timed Automata

Kwiatkowska

Norman

Parker

2017

Abstract. Probabilistic timed automata are a formalism for modelling systems whose dynamics includes probabilistic, nondeterministic and timed aspects including real-time systems. A variety of techniques have been proposed for the analysis of this formalism and successfully employed to analyse, for example, wireless communication protocols and computer security systems. Augmenting the model with prices (or, equivalently, costs or rewards) provides a means to verify more complex quantitative properties, such as the expected energy usage of a device or the expected number of messages sent during a protocol's execution. However, the analysis of these properties on probabilistic timed automata currently relies on a technique based on integer discretisation of real-valued clocks, which can be expensive in some cases. In this paper, we propose symbolic techniques for verification and optimal strategy synthesis for priced probabilistic timed automata which avoid this discretisation. We build upon recent work for the special case of expected time properties, using value iteration over a zone-based abstraction of the model.