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36
On probabilistic model checking
, 1996
"... Abstract. This tutorial presents an overview of model checking for both discrete and continuoustime 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 ..."
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Cited by 106 (26 self)
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Abstract. This tutorial presents an overview of model checking for both discrete and continuoustime 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 realworld case studies: a probabilistic security protocol, dynamic power management and a biological pathway. 1
Automated Verification Techniques for Probabilistic Systems
"... Abstract. 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 ..."
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Cited by 40 (17 self)
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Abstract. 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 rewardbased measures. We also discuss multiobjective probabilistic model checking, used to analyse tradeoffs 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 multicomponent probabilistic systems. Finally, we describe three large case studies which illustrate practical applications of the various methods discussed in the tutorial. 1
Statistical model checking: An overview
 RV 2010
, 2010
"... Quantitative properties of stochastic systems are usually specified in logics that allow one to compare the measure of executions satisfying certain temporal properties with thresholds. The model checking problem for stochastic systems with respect to such logics is typically solved by a numerical a ..."
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Cited by 28 (6 self)
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Quantitative properties of stochastic systems are usually specified in logics that allow one to compare the measure of executions satisfying certain temporal properties with thresholds. The model checking problem for stochastic systems with respect to such logics is typically solved by a numerical approach [31,8,35,22,21,5] that iteratively computes (or approximates) the exact measure of paths satisfying relevant subformulas; the algorithms themselves depend on the class of systems being analyzed as well as the logic used for specifying the properties. Another approach to solve the model checking problem is to simulate the system for finitely many executions, and use hypothesis testing to infer whether the samples provide a statistical evidence for the satisfaction or violation of the specification. In this tutorial, we survey the statistical approach, and outline its main advantages in terms of efficiency, uniformity, and simplicity.
Minimal critical subsystems for discretetime Markov models
 IN: PROC. OF TACAS. VOL. 7214 OF LNCS
, 2012
"... We propose a new approach to compute counterexamples for violated ωregular properties of discretetime Markov chains and Markov decision processes. Whereas most approaches compute a set of system paths as a counterexample, we determine a critical subsystem that already violates the given property. ..."
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Cited by 13 (6 self)
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We propose a new approach to compute counterexamples for violated ωregular properties of discretetime Markov chains and Markov decision processes. Whereas most approaches compute a set of system paths as a counterexample, we determine a critical subsystem that already violates the given property. In earlier work we introduced methods to compute such subsystems based on a search for shortest paths. In this paper we use SMT solvers and mixed integer linear programming to determine minimal critical subsystems.
Best Probabilistic Transformers
"... Abstract. This paper investigates relative precision and optimality of analyses for concurrent probabilistic systems. Aiming at the problem at the heart of probabilistic model checking – computing the probability of reaching a particular set of states – we leverage the theory of abstract interpretat ..."
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Cited by 10 (2 self)
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Abstract. This paper investigates relative precision and optimality of analyses for concurrent probabilistic systems. Aiming at the problem at the heart of probabilistic model checking – computing the probability of reaching a particular set of states – we leverage the theory of abstract interpretation. With a focus on predicate abstraction, we develop the first abstractinterpretation framework for Markov decision processes which admits to compute both lower and upper bounds on reachability probabilities. Further, we describe how to compute and approximate such abstractions using abstraction refinement and give experimental results. 1
A linear processalgebraic format with data for probabilistic automata
, 2011
"... This paper presents a novel linear processalgebraic format for probabilistic automata. The key ingredient is a symbolic transformation of probabilistic process algebra terms that incorporate data into this linear format while preserving strong probabilistic bisimulation. This generalises similar te ..."
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Cited by 6 (4 self)
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This paper presents a novel linear processalgebraic format for probabilistic automata. The key ingredient is a symbolic transformation of probabilistic process algebra terms that incorporate data into this linear format while preserving strong probabilistic bisimulation. This generalises similar techniques for traditional process algebras with data, and — more importantly — treats data and datadependent probabilistic choice in a fully symbolic manner, leading to the symbolic analysis of parameterised probabilistic systems. We discuss several reduction techniques that can easily be applied to our models. A validation of our approach on two benchmark leader election protocols shows reductions of more than an order of magnitude.
A counterexample guided abstractionrefinement framework for Markov decision processes
 ACM TRANSACTIONS ON COMPUTATIONAL LOGIC
, 2010
"... The main challenge in using abstractions effectively, is to construct a suitable abstraction for the system being verified. One approach that tries to address this problem is that of counterexample guided abstractionrefinement (CEGAR), wherein one starts with a coarse abstraction of the system, and ..."
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Cited by 5 (0 self)
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The main challenge in using abstractions effectively, is to construct a suitable abstraction for the system being verified. One approach that tries to address this problem is that of counterexample guided abstractionrefinement (CEGAR), wherein one starts with a coarse abstraction of the system, and progressively refines it, based on invalid counterexamples seen in prior model checking runs, until either an abstraction proves the correctness of the system or a valid counterexample is generated. While CEGAR has been successfully used in verifying nonprobabilistic systems automatically, CEGAR has not been applied in the context of probabilistic systems. The main issues that need to be tackled in order to extend the approach to probabilistic systems is a suitable notion of “counterexample”, algorithms to generate counterexamples, check their validity, and then automatically refine an abstraction based on an invalid counterexample. In this paper, we address these issues, and present a CEGAR framework for Markov Decision Processes.
Probabilistic abstractions with arbitrary domains
 In SAS, volume 6887 of LNCS
, 2011
"... All intext references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately. ..."
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Cited by 5 (1 self)
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All intext references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately.
Highlevel Counterexamples for Probabilistic Automata
"... Abstract. Providing compact and understandable counterexamples for violated system properties is an essential task in model checking. Existing works on counterexamples for probabilistic systems so far computed either a large set of system runs or a subset of the system’s states, both of which are of ..."
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Cited by 5 (1 self)
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Abstract. Providing compact and understandable counterexamples for violated system properties is an essential task in model checking. Existing works on counterexamples for probabilistic systems so far computed either a large set of system runs or a subset of the system’s states, both of which are of limited use in manual debugging. Many probabilistic systems are described in a guarded command language like the one used by the popular model checker PRISM. In this paper we describe how a minimal subset of the commands can be identified which together already make the system erroneous. We additionally show how the selected commands can be further simplified to obtain a wellunderstandable counterexample. 1
Verification and Refutation of Probabilistic Specifications via Games
 LIPICS LEIBNIZ INTERNATIONAL PROCEEDINGS IN INFORMATICS
, 2009
"... We develop an abstractionbased framework to check probabilistic specifications of Markov Decision Processes (MDPs) using the stochastic twoplayer game abstractions (i.e. “games”) developed by Kwiatkowska et al. as a foundation. We define an abstraction preorder for these game abstractions which e ..."
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Cited by 4 (1 self)
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We develop an abstractionbased framework to check probabilistic specifications of Markov Decision Processes (MDPs) using the stochastic twoplayer game abstractions (i.e. “games”) developed by Kwiatkowska et al. as a foundation. We define an abstraction preorder for these game abstractions which enables us to identify many new game abstractions for each MDP — ranging from compact and imprecise to complex and precise. This added ability to trade precision for efficiency is crucial for scalable software model checking, as precise abstractions are expensive to construct in practice. Furthermore, we develop a fourvalued probabilistic computation tree logic (PCTL) semantics for game abstractions. Together, the preorder and PCTL semantics comprise a powerful verification and refutation framework for arbitrary PCTL properties of MDPs.