Marta Z. Kwiatkowska

PRISM 4.0: verification of probabilistic real-time systems

This paper describes a major new release of the PRISMprobabilistic 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.

PRISM: a tool for automatic verification of probabilistic systems

Probabilistic model checking is an automatic formal verification technique for analysing quantitative properties of systems which exhibit stochastic behaviour. PRISM is a probabilistic model checking tool which has already been successfully deployed in a wide range of application domains, from real-time communication protocols to biological signalling pathways. The tool has recently undergone a significant amount of development. Major additions include facilities to manually explore models, Monte-Carlo discrete-event simulation techniques for approximate model analysis (including support for distributed simulation) and the ability to compute cost- and reward-based measures, e.g. “the expected energy consumption of the system before the first failure occurs”. This paper presents an overview of all the main features of PRISM. More information can be found on the website: www.cs.bham.ac.uk/~dxp/prism.

PRISM: Probabilistic Symbolic Model Checker

In this paper we describe PRISM, a tool being developed at the University of Birmingham for the analysis of probabilistic systems. PRISM supports three probabilistic models: discrete-time Markov chains, Markov decision processes and continuous-time Markov chains. Analysis is performed through model checking such systems against specifications written in the probabilistic temporal logics PCTL and CSL. The tool features three model checking engines: one symbolic, using BDDs (binary decision diagrams) and MTBDDs (multi-terminal BDDs); one based on sparse matrices; and one which combines both symbolic and sparse matrix methods. PRISM has been successfully used to analyse probabilistic termination, performance, and quality of service properties for a range of systems, including randomized distributed algorithms, manufacturing systems and workstation clusters.

Probabilistic Symbolic Model Checking with PRISM: A Hybrid Approach

In this paper we present efficient symbolic techniques for probabilistic model checking. These have been implemented in PRISM, a tool for the analysis of probabilistic models such as discrete-time Markov chains, continuous-time Markov chains and Markov decision processes using specifications in the probabilistic temporal logics PCTL and CSL. Motivated by the success of model checkers such as SMV which use BDDs (binary decision diagrams), we have developed an implementation of PCTL and CSL model checking based on MTBDDs (multi-terminal BDDs) and BDDs. Existing work in this direction has been hindered by the generally poor performance of MTBDD-based numerical computation, which is often substantially slower than explicit methods using sparse matrices. The focus of this paper is a novel hybrid technique which combines aspects of symbolic and explicit approaches to overcome these performance problems. For typical examples, we achieve a dramatic improvement over the purely symbolic approach. In addition, thanks to the compact model representation using MTBDDs, we can verify systems an order of magnitude larger than with sparse matrices, while almost matching or even beating them for speed.

Stochastic model checking

This tutorial presents an overview of model checking for both discrete and continuous-time Markov chains (DTMCs and CTMCs). Model checking algorithms are given for verifying DTMCs and CTMCs against specifications written in probabilistic extensions of temporal logic, including quantitative properties with rewards. Example properties include the probability that a fault occurs and the expected number of faults in a given time period. We also describe the practical application of stochastic model checking with the probabilistic model checker PRISM by outlining the main features supported by PRISM and three real-world case studies: a probabilistic security protocol, dynamic power management and a biological pathway.

Automatic verification of real-time systems with discrete probability distributions

We consider the timed automata model of Alur and Dill (Theoret. Comput. Sci. 126 (1994) 183-235), 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, it is often desirable 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, two approaches to model checking are introduced for this model. The first uses the algorithm of Baier and Kwiatkowska (Distributed Comput. 11 (1998) 125-155) to provide a verification technique against temporal logic formulae which can refer both to timing properties and probabilities. The second, generally more efficient, technique concerns the verification of probabilistic, real-time reachability properties.

Dynamic QoS Management and Optimization in Service-Based Systems

Service-based systems that are dynamically composed at runtime to provide complex, adaptive functionality are currently one of the main development paradigms in software engineering. However, the Quality of Service (QoS) delivered by these systems remains an important concern, and needs to be managed in an equally adaptive and predictable way. To address this need, we introduce a novel, tool-supported framework for the development of adaptive service-based systems called QoSMOS (QoS Management and Optimization of Service-based systems). QoSMOS can be used to develop service-based systems that achieve their QoS requirements through dynamically adapting to changes in the system state, environment, and workload. QoSMOS service-based systems translate high-level QoS requirements specified by their administrators into probabilistic temporal logic formulae, which are then formally and automatically analyzed to identify and enforce optimal system configurations. The QoSMOS self-adaptation mechanism can handle reliability and performance-related QoS requirements, and can be integrated into newly developed solutions or legacy systems. The effectiveness and scalability of the approach are validated using simulations and a set of experiments based on an implementation of an adaptive service-based system for remote medical assistance.

Probabilistic model checking of complex biological pathways

Probabilistic model checking is a formal verification technique that has been successfully applied to the analysis of systems from a broad range of domains, including security and communication protocols, distributed algorithms and power management. In this paper we illustrate its applicability to a complex biological system: the FGF (Fibroblast Growth Factor) signalling pathway. We give a detailed description of how this case study can be modelled in the probabilistic model checker PRISM, discussing some of the issues that arise in doing so, and show how we can thus examine a rich selection of quantitative properties of this model. We present experimental results for the case study under several different scenarios and provide a detailed analysis, illustrating how this approach can be used to yield a better understanding of the dynamics of the pathway. Finally, we outline a number of exact and approximate techniques to enable the verification of larger and more complex pathways and apply several of them to the FGF case study.

Model checking for a probabilistic branching time logic with fairness

Abstract. We consider concurrent probabilistic systems, based on probabilistic automata of Segala & Lynch [55], which allow non-deterministic choice between probability distributions. These systems can be decomposed into a collection of “computation trees” which arise by resolving the non-deterministic, but not probabilistic, choices. The presence of non-determinism means that certain liveness properties cannot be established unless fairness is assumed. We introduce a probabilistic branching time logic PBTL, based on the logic TPCTL of Hansson [30] and the logic PCTL of [55], resp. pCTL [14]. The formulas of the logic express properties such as “every request is eventually granted with probability at least p”. We give three interpretations for PBTL on concurrent probabilistic processes: the first is standard, while in the remaining two interpretations the branching time quantifiers are taken to range over a certain kind of fair computation trees. We then present a model checking algorithm for verifying whether a concurrent probabilistic process satisfies a PBTL formula assuming fairness constraints. We also propose adaptations of existing model checking algorithms for pCTL

PRISM: probabilistic model checking for performance and reliability analysis

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