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30
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
Gamebased abstraction for Markov decision processes
, 2006
"... In this paper we present a novel abstraction technique for Markov decision processes (MDPs), which are widely used for modelling systems that exhibit both probabilistic and nondeterministic behaviour. In the field of model checking, abstraction has proved an extremely successful tool to combat the s ..."
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Cited by 55 (16 self)
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In this paper we present a novel abstraction technique for Markov decision processes (MDPs), which are widely used for modelling systems that exhibit both probabilistic and nondeterministic behaviour. In the field of model checking, abstraction has proved an extremely successful tool to combat the statespace explosion problem. In the probabilistic setting, however, little practical progress has been made in this area. We propose an abstraction method for MDPs based on stochastic twoplayer games. The key idea behind this approach is to maintain a separation between nondeterminism present in the original MDP and nondeterminism introduced through abstraction, each type being represented by a different player in the game. Crucially, this allows us to obtain distinct lower and upper bounds for both the best and worstcase performance (minimum or maximum probabilities) of the MDP. We have implemented our techniques and illustrate their practical utility by applying them to a quantitative analysis of the Zeroconf dynamic network configuration protocol. 1.
A gamebased abstractionrefinement framework for
 Markov Decision Processes. Formal Methods in System Design 36(3):246–280
, 2010
"... In the field of model checking, abstraction refinement has proved to be an extremely successful methodology for combating the statespace explosion problem. However, little practical progress has been made in the setting of probabilistic verification. In this paper we present a novel abstractionr ..."
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Cited by 22 (15 self)
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In the field of model checking, abstraction refinement has proved to be an extremely successful methodology for combating the statespace explosion problem. However, little practical progress has been made in the setting of probabilistic verification. In this paper we present a novel abstractionrefinement framework for Markov decision processes (MDPs), which are widely used for modelling and verifying systems that exhibit both probabilistic and nondeterministic behaviour. Our framework comprises an abstraction approach based on stochastic twoplayer games, two refinement methods and an efficient algorithm for the abstractionrefinement loop. The key idea behind the abstraction approach is to maintain a separation between nondeterminism present in the original MDP and nondeterminism introduced during the abstraction process, each type being represented by a different player in the game. Crucially, this allows lower and upper bounds to be computed for the values of reachability properties of the MDP. These give a quantitative measure of the quality of the abstraction and form the basis of the corresponding refinement methods. We describe a prototype implementation of our framework and present experimental results demonstrating automatic generation of compact, yet precise, abstractions for a large selection of realworld case studies. 1
Partial Order Reduction For Probabilistic Branching Time
, 2005
"... In the past, partial order reduction has been used successfully to combat the state explosion problem in the context of model checking for nonprobabilistic systems. For both linear time and branching time specifications, methods have been developed to apply partial order reduction in the context of ..."
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Cited by 16 (3 self)
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In the past, partial order reduction has been used successfully to combat the state explosion problem in the context of model checking for nonprobabilistic systems. For both linear time and branching time specifications, methods have been developed to apply partial order reduction in the context of model checking. Only recently, results were published that give criteria on applying partial order reduction for verifying quantitative linear time properties for probabilistic systems. This paper presents partial order reduction criteria for Markov decision processes and branching time properties, such as formulas of probabilistic computation tree logic. Moreover, we provide a comparison of the results established so far about reduction conditions for Markov decision processes.
Partial order reduction for probabilistic systems assuming distributed schedulers
 Serie A, Inf. 2009/02, FaMAF, UNC, 2009. Available at
"... Abstract. In the verification of probabilistic systems, distributed schedulers are used to obtain tight bounds on worstcase probabilities, these bounds being more realistic than the ones obtained by considering unrestricted fullhistory dependent schedulers. In this paper, we define two classes o ..."
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Cited by 10 (1 self)
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Abstract. In the verification of probabilistic systems, distributed schedulers are used to obtain tight bounds on worstcase probabilities, these bounds being more realistic than the ones obtained by considering unrestricted fullhistory dependent schedulers. In this paper, we define two classes of distributed schedulers. We present undecidability results related to the automatic verification under these classes of schedulers. In previous literature, we have proven that the model checking problem is undecidable for distributed schedulers. However, in this paper we show that, by assuming that the schedulers are in a given class, the technique of partial order reduction (POR) for LTL properties can be applied in a more efficient way than usual, thus yielding a system with less states and transitions than if reduced assuming unrestricted schedulers. The reduced system can then be analysed using wellknown algorithms for fullhistory dependent schedulers. Our partial order reduction technique may also obtain bounds strictly tighter than the ones obtained by considering unrestricted schedulers (of course, such bounds are safe with respect to the class of schedulers under consideration). We explain that the two variants we present are obtained from a general theorem, thus raising the question of whether there are other “natural ” classes of schedulers for which POR variants can be developed. 1
Partial order reduction for model checking Markov decision processes under unconditional
, 2012
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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 7 (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.
Quantitative Analysis of Distributed Randomized Protocols
, 2005
"... A wide range of coordination protocols for distributed systems, internet protocols or systems with unreliable components can formally be modelled by Markov decision processes (MDP). MDPs can be viewed as a variant of statetransition diagrams with discrete probabilities and nondeterminism. While tra ..."
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Cited by 4 (0 self)
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A wide range of coordination protocols for distributed systems, internet protocols or systems with unreliable components can formally be modelled by Markov decision processes (MDP). MDPs can be viewed as a variant of statetransition diagrams with discrete probabilities and nondeterminism. While traditional model checking techniques for nonprobabilistic systems aim to establish properties stating that all (or some) computations fulfill a certain condition, the verification problem for randomized systems requires reasoning about the quantitative behavior by means of properties that refer to the probabilities for certain computations, for instance, the probability to find a leader within 5 rounds or the probability for not reaching an error state.
Onthefly Confluence Detection for Statistical Model Checking
, 2013
"... Statistical model checking is an analysis method that circumvents the state space explosion problem in modelbased verification by combining probabilistic simulation with statistical methods that provide clear error bounds. As a simulationbased technique, it can only provide sound results if the un ..."
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Cited by 4 (2 self)
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Statistical model checking is an analysis method that circumvents the state space explosion problem in modelbased verification by combining probabilistic simulation with statistical methods that provide clear error bounds. As a simulationbased technique, it can only provide sound results if the underlying model is a stochastic process. In verification, however, models are usually variations of nondeterministic transition systems. The notion of confluence allows the reduction of such transition systems in classical model checking by removing spurious nondeterministic choices. In this presentation, we show that confluence can be adapted to detect and discard such choices onthefly during simulation, thus extending the applicability of statistical model checking to a subclass of Markov decision processes. In contrast to previous approaches that use partial order reduction, the confluencebased technique can handle additional kinds of nondeterminism. In particular, it is not restricted to interleavings. We evaluate our approach, which is implemented as part of the modes simulator for the MODEST modelling language, on a set of examples that highlight its strengths and limitations and show the improvements compared to the partial orderbased method.
Computing expected absorption times for parametric determinate probabilistic timed automata
, 2008
"... We consider a variant of probabilistic timed automata called parametric determinate probabilistic timed automata. Such automata are fully probabilistic: there is a single distribution of outgoing transitions from each of the automaton’s nodes, and it is possible to remain at a node only for a given ..."
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Cited by 3 (1 self)
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We consider a variant of probabilistic timed automata called parametric determinate probabilistic timed automata. Such automata are fully probabilistic: there is a single distribution of outgoing transitions from each of the automaton’s nodes, and it is possible to remain at a node only for a given amount of time. The residence time within a node may be given in terms of a parameter, and hence we do not assume that its concrete value is known. We claim that, often in practice, the maximal expected time to reach a given absorbing node of a probabilistic timed automaton can be captured using a parametric determinate probabilistic timed automaton. We give a method for computing the expected time for a parametric determinate probabilistic timed automaton to reach an absorbing node. The method consists in constructing a variant of a Markov chain with costs (where the costs correspond to durations), and is parametric in the sense that the expected absorption time is computed as a function of the model’s parameters. The complexity of the analysis is independent from the maximal constant bounding the values of the clocks, and is polynomial in the number of edges of the original parametric determinate probabilistic timed automaton. 1