Assume-guarantee verification for probabilistic systems

2010

We present a fully automated technique for compositional verification of probabilistic systems. Our approach builds upon a recently proposed assume-guarantee framework for probabilistic automata, in which assumptions and guarantees are probabilistic safety properties, represented using finite automata. A limitation of this work is that the assumptions need to be created manually. To overcome this, we propose a novel learning technique based on the L* algorithm, which automatically generates probabilistic assumptions using the results of queries executed by a probabilistic model checker. Learnt assumptions either establish satisfaction of the verification problem or are used to generate a probabilistic counterexample that refutes it. In the case where an assumption cannot be generated, lower and upper bounds on the probability of satisfaction are produced. We illustrate the applicability of the approach on a range of case studies.

2011

This tutorial provides an introduction to probabilistic model checking, a technique for automatically verifying quantitative properties of probabilistic systems. We focus on Markov decision processes (MDPs), which model both stochastic and nondeterministic behaviour. We describe methods to analyse a wide range of their properties, including specifications in the temporal logics PCTL and LTL, probabilistic safety properties and cost-or reward-based measures. We also discuss multiobjective probabilistic model checking, used to analyse trade-offs between several different quantitative properties. Applications of the techniques in this tutorial include performance and dependability analysis of networked systems, communication protocols and randomised distributed algorithms. Since such systems often comprise several components operating in parallel, we also cover techniques for compositional modelling and verification of multi-component probabilistic systems. Finally, we describe three large case studies which illustrate practical applications of the various methods discussed in the tutorial.

2011

We present a verification framework for analysing multiple quantitative objectives of systems that exhibit both nondeterministic and stochastic behaviour. These systems are modelled as probabilistic automata, enriched with cost or reward structures that capture, for example, energy usage or performance metrics. Quantitative properties of these models are expressed in a specification language that incorporates probabilistic safety and liveness properties, expected total cost or reward, and supports multiple objectives of these types. We propose and implement an efficient verification framework for such properties and then present two distinct applications of it: firstly, controller synthesis subject to multiple quantitative objectives; and, secondly, quantitative compositional verification. The practical applicability of both approaches is illustrated with experimental results from several large case studies.

2008

Abstract Soon after the birth of the flourishing research area of model checking in the early eighties, researchers started to apply this technique to finite automata equipped with probabilities. The initial focus was on qualitative properties-eg, does a program terminate with probability one?-but later efficient algorithms were developed for quantitative questions as well. Model checking of probabilistic models received quite some attention in the late nineties, and this popularity lasts until today.

Formal Methods in System Design, 2010

A contract allows to distinguish hypotheses made on a system (the guarantees) from those made on its environment (the assumptions). In this paper, we focus on models of Assume/Guarantee contracts for (stochastic) systems. We consider contracts capable of capturing reliability and availability properties of such systems. We also show that classical notions of Satisfaction and Refinement can be checked by effective methods thanks to a reduction to classical verification problems. Finally, theorems supporting compositional reasoning and enabling the scalable analysis of complex systems are also studied.

2010

Quantitative verification techniques are able to establish system properties such as "the probability of an airbag failing to deploy on demand" or "the expected time for a network protocol to successfully send a message packet". In this paper, we describe a framework for quantitative verification of software that exhibits both real-time and probabilistic behaviour. The complexity of real software, combined with the need to capture precise timing information, necessitates the use of abstraction techniques. We outline a quantitative abstraction refinement approach, which can be used to automatically construct and analyse abstractions of probabilistic, real-time programs. As a concrete example of the potential applicability of our framework, we discuss the challenges involved in applying it to the quantitative verification of SystemC, an increasingly popular system-level modelling language.

Lecture Notes in Computer Science, 2003

The paper studies automatic verification of liveness properties with probability 1 over parameterized programs that include probabilistic transitions, and proposes two novel approaches to the problem. The first approach is based on a Planner that occasionally determines the outcome of a finite sequence of "random" choices, while the other random choices are performed non-deterministically. Using a Planner, a probabilistic protocol can be treated just like a non-probabilistic one and verified as such. The second approach is based on γ-fairness, a notion of fairness that is sound and complete for verifying simple temporal properties (whose only temporal operators are ½ and ¼ ) over finite-state systems. The paper presents a symbolic model checker based on γ-fairness. We then show how the network invariant approach can be adapted to accommodate probabilistic protocols. The utility of the Planner approach is demonstrated on a probabilistic mutual exclusion protocol. The utility of the approach of γ-fairness with network invariants is demonstrated on Lehman and Rabin's Courteous Philosophers algorithm. ⋆

2011

Abstract: Research efforts were conducted under this task order to emphasize unique technologies in support of achieving the program goals associated with the META Program. The contractor focused on technologies and technological breakthroughs addressing probabilistic verification of cyber physical system aspects. Collaboration with Honeywell International Inc., Aerospace, TTTech Computertechnik AG, and Vanderbilt University was facilitated to optimize technology development.

2012

Abstract—We address the problem of verifying PCTL properties of Markov Decision Processes whose state transition probabilities are only known to lie within uncertainty sets. Using results from convex theory and duality, we propose a suite of verication algorithms and prove their soundness, completeness and termination when arbitrary convex models of uncertainty are considered. Furthermore, soundness and termination can also be guaranteed when non-convex models of uncertainty are adopted.

2011

This paper describes a major new release of the PRISM probabilistic model checker, adding, in particular, quantitative verification of (priced) probabilistic timed automata. These model systems exhibiting probabilistic, nondeterministic and real-time characteristics. In many application domains, all three aspects are essential; this includes, for example, embedded controllers in automotive or avionic systems, wireless communication protocols such as Bluetooth or Zigbee, and randomised security protocols. PRISM, which is open-source, also contains several new components that are of independent use. These include: an extensible toolkit for building, verifying and refining abstractions of probabilistic models; an explicit-state probabilistic model checking library; a discrete-event simulation engine for statistical model checking; support for generation of optimal adversaries/strategies; and a benchmark suite.