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29
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 107 (25 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 (16 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
Probabilistic Analysis of Correctness of HighLevel Robot Behavior with Sensor Error
"... Abstract—This paper presents a method for reasoning about the effects of sensor error on highlevel robot behavior. We consider robot controllers that are synthesized from a set of highlevel, temporal logic task specifications, such that the resulting robot behavior is guaranteed to satisfy these sp ..."
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Cited by 16 (1 self)
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Abstract—This paper presents a method for reasoning about the effects of sensor error on highlevel robot behavior. We consider robot controllers that are synthesized from a set of highlevel, temporal logic task specifications, such that the resulting robot behavior is guaranteed to satisfy these specifications when assuming perfect sensors and actuators. We relax the assumption of perfect sensing, and calculate the probability with which the controller satisfies a set of temporal logic specifications. We consider parametric representations, where the satisfaction probability is found as a function of the model parameters, and numerical representations, allowing for the analysis of large examples. We illustrate our approach with three examples of varying size that provide insight into unintuitive effects of sensor error that can inform the specification design process. I.
Model Repair for Probabilistic Systems
"... Abstract. We introduce the problem of Model Repair for Probabilistic Systems as follows. Given a probabilistic system M and a probabilistic temporal logic formula φ such that M fails to satisfy φ, the Model Repair problem is to find an M ′ that satisfies φ and differs from M only in the transition f ..."
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Cited by 12 (2 self)
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Abstract. We introduce the problem of Model Repair for Probabilistic Systems as follows. Given a probabilistic system M and a probabilistic temporal logic formula φ such that M fails to satisfy φ, the Model Repair problem is to find an M ′ that satisfies φ and differs from M only in the transition flows of those states in M that are deemed controllable. Moreover, the cost associated with modifying M’s transition flows to obtain M ′ should be minimized. We show how the Model Repair problem can be formulated as an extended version of parametric probabilistic model checking, which translates into a nonlinear optimization problem with a minimalcost objective function, thereby yielding a solution technique. We demonstrate the practical utility of our approach by applying it to a number of significant case studies, including a DTMC reward model of the Zeroconf protocol for assigning IP addresses, and a CTMC model of the highly publicized Kaminsky DNS cachepoisoning attack.
PARAM: A model checker for parametric markov models
 In Proceedings of the 22nd International Conference on Computer Aided Verification(CAV 2010
, 2010
"... Abstract. We present PARAM 1.0, a model checker for parametric discretetime Markov chains (PMCs). PARAM can evaluate temporal properties of PMCs and certain extensions of this class. Due to parametricity, evaluation results are polynomials or rational functions. By instantiating the parameters in t ..."
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Cited by 12 (3 self)
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Abstract. We present PARAM 1.0, a model checker for parametric discretetime Markov chains (PMCs). PARAM can evaluate temporal properties of PMCs and certain extensions of this class. Due to parametricity, evaluation results are polynomials or rational functions. By instantiating the parameters in the result function, one can cheaply obtain results for multiple individual instantiations, based on only a single more expensive analysis. In addition, it is possible to postprocess the result function symbolically using for instance computer algebra packages, to derive optimum parameters or to identify worst cases. 1 Introducing PARAM Markov processes are applied in computer science, engineering, mathematics, and biology. In the early design phase of a system or for the sake of robust modelling, it can be advantageous to leave certain aspects unspecified
Synthesis for PCTL in parametric Markov decision processes.
 In NASA Formal Methods (NFM),
, 2011
"... Abstract. In parametric Markov Decision Processes (PMDPs), transition probabilities are not fixed, but are given as functions over a set of parameters. A PMDP denotes a family of concrete MDPs. This paper studies the synthesis problem for PCTL in PMDPs: Given a specification Φ in PCTL, we synthesis ..."
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Cited by 9 (2 self)
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Abstract. In parametric Markov Decision Processes (PMDPs), transition probabilities are not fixed, but are given as functions over a set of parameters. A PMDP denotes a family of concrete MDPs. This paper studies the synthesis problem for PCTL in PMDPs: Given a specification Φ in PCTL, we synthesise the parameter valuations under which Φ is true. First, we divide the possible parameter space into hyperrectangles. We use existing decision procedures to check whether Φ holds on each of the Markov processes represented by the hyperrectangle. As it is normally impossible to cover the whole parameter space by hyperrectangles, we allow a limited area to remain undecided. We also consider an extension of PCTL with reachability rewards. To demonstrate the applicability of the approach, we apply our technique on a case study, using a preliminary implementation.
Advances and Challenges of Probabilistic Model Checking
 48TH ANNUAL ALLERTON CONFERENCE ON COMMUNICATION, CONTROL AND COMPUTING (2010) 16911698
, 2010
"... Probabilistic model checking is a powerful technique for formally verifying quantitative properties of systems that exhibit stochastic behaviour. Such systems are found in many domains: probabilistic behaviour may arise, for example, due to failures of unreliable components, communication across los ..."
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Cited by 8 (0 self)
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Probabilistic model checking is a powerful technique for formally verifying quantitative properties of systems that exhibit stochastic behaviour. Such systems are found in many domains: probabilistic behaviour may arise, for example, due to failures of unreliable components, communication across lossy media, or through the use of randomisation in distributed protocols. In this paper, we give a short overview of probabilistic model checking and of PRISM (www.prismmodelchecker.org), currently the leading software tool in this area. We then mention some of the limitations of these techniques, describe some of the advances that are being made to overcome them, and outline key challenges that remain in this research area.
Further steps towards efficient runtime verification: Handling probabilistic cost models
 doi: 10 . 1109 / FormSERA
"... AbstractWe consider highlevel models that specify system behaviors probabilistically and support the specification of cost attributes. Specifically, we focus on Discrete Time Markov Reward Models (DMRMs), i.e. state machines where probabilities can be associated with transitions and rewards (cos ..."
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Cited by 6 (5 self)
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AbstractWe consider highlevel models that specify system behaviors probabilistically and support the specification of cost attributes. Specifically, we focus on Discrete Time Markov Reward Models (DMRMs), i.e. state machines where probabilities can be associated with transitions and rewards (costs) can be associated with states and transitions. Through probabilities we model assumptions on the behavior of environment in which an application is embedded. Rewards can instead model the cost assumptions involved in the system's operations. A system is designed to satisfy the requirements, under the given assumptions. Designtime assumptions, however, can turn out to be invalid at runtime, and therefore it is necessary to verify whether changes may lead to requirements violations. If they do, it is necessary to adapt the behavior in a selfhealing manner to continue to satisfy the requirements. We have previously presented an approach to support efficient runtime probabilistic model checking of DTMCs for properties expressed in PCTL. In this paper we extend the approach to DMRMs and reward properties. The benefits of the approach are justified both theoretically and empirically on significant test cases.
Model Repair for Markov Decision Processes
"... Abstract—Markov decision processes (MDPs) are often used for modelling distributed systems with probabilistic failure or randomisation. We consider the problem of model repair for MDPs defined as follows: if the MDP fails to satisfy a property, we aim to find new values for the transition probabilit ..."
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Cited by 5 (3 self)
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Abstract—Markov decision processes (MDPs) are often used for modelling distributed systems with probabilistic failure or randomisation. We consider the problem of model repair for MDPs defined as follows: if the MDP fails to satisfy a property, we aim to find new values for the transition probabilities so that the property is guaranteed to hold, while at the same time the cost of repair is minimised. Because solving the MDP repair problem exactly is infeasible, in this paper we focus on approximate solution methods. We first formulate a regionbased approach, which yields an interval in which the minimal repair cost is contained. As an alternative, we also consider samplingbased approaches, which are faster but unable to provide lower bounds on the repair cost. We have integrated both methods into the probabilistic model checker PRISM and demonstrated their usefulness in practice using a computer virus case study. I.
SMTbased bisimulation minimisation of markov models
 In VMCAI, volume 7737 of LNCS
, 2013
"... Abstract. Probabilistic model checking is an increasingly widely used formal verification technique. However, its dependence on computationally expensive numerical operations makes it particularly susceptible to the statespace explosion problem. Among other abstraction techniques, bisimulation min ..."
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Cited by 4 (1 self)
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Abstract. Probabilistic model checking is an increasingly widely used formal verification technique. However, its dependence on computationally expensive numerical operations makes it particularly susceptible to the statespace explosion problem. Among other abstraction techniques, bisimulation minimisation has proven to shorten computation times significantly, but, usually, the full state space needs to be built prior to minimisation. We present a novel approach that leverages satisfiability solvers to extract the minimised system from a highlevel description directly. A prototypical implementation in the framework of the probabilistic model checker Prism provides encouraging experimental results. 1