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Probabilistic Symbolic Model Checking with PRISM: A Hybrid Approach
 International Journal on Software Tools for Technology Transfer (STTT
, 2002
"... In this paper we introduce PRISM, a probabilistic model checker, and describe the ecient symbolic techniques we have developed during its implementation. PRISM is a tool for analysing probabilistic systems. It supports three models: discretetime Markov chains, continuoustime Markov chains and ..."
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Cited by 207 (32 self)
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In this paper we introduce PRISM, a probabilistic model checker, and describe the ecient symbolic techniques we have developed during its implementation. PRISM is a tool for analysing probabilistic systems. It supports three models: discretetime Markov chains, continuoustime Markov chains and Markov decision processes. Analysis is performed through model checking speci cations 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 (multiterminal BDDs) and BDDs. Existing work in this direction has been hindered by the generally poor performance of MTBDDbased numerical computation, which is often substantially slower than explicit methods using sparse matrices. We present a novel hybrid technique which combines aspects of symbolic and explicit approaches to overcome these performance problems. For typical examples, we achieve orders of magnitude speedup compared to MTBDDs and are able to almost match the speed of sparse matrices whilst maintaining considerable space savings.
Automatic verification of realtime systems with discrete probability distributions
 Theoretical Computer Science
, 1999
"... Abstract. We consider the timed automata model of [3], which allows the analysis of realtime systems expressed in terms of quantitative timing constraints. Traditional approaches to realtime system description express the model purely in terms of nondeterminism; however, we may wish to express the ..."
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Cited by 118 (33 self)
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Abstract. We consider the timed automata model of [3], which allows the analysis of realtime systems expressed in terms of quantitative timing constraints. Traditional approaches to realtime system description express the model purely in terms of nondeterminism; however, we may wish to express the likelihood of the system making certain transitions. In this paper, we present a model for realtime systems augmented with discrete probability distributions. Furthermore, using the algorithm of [5] with fairness, we develop a model checking method for such models against temporal logic properties which can refer both to timing properties and probabilities, such as, “with probability 0.6 or greater, the clock x remains below 5 until clock y exceeds 2”. 1
Symbolic Model Checking of Probabilistic Timed Automata Using Backwards Reachability
, 2000
"... We consider probabilistic timed automata of [13], an extension of the timed automata model of [2] with discrete probability distributions. In contrast to timed automata, which model realtime systems purely in terms of nondeterminism, our model allows to express the likelihood of the system makin ..."
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Cited by 82 (26 self)
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We consider probabilistic timed automata of [13], an extension of the timed automata model of [2] with discrete probability distributions. In contrast to timed automata, which model realtime systems purely in terms of nondeterminism, our model allows to express the likelihood of the system making certain transitions, and is thus appropriate for modelling faulttolerance and probabilistic failures. We present a symbolic model checking algorithm for the existential fragment of the logic PTCTL of [13] based on backward reachability as in [12]. The logic allows us to specify properties such as \with probability 0.99 or greater, it is possible to correctly deliver a data packet within 5 time units", or \with probability 0.87 or greater, the system never enters an error state".
Performance analysis of probabilistic timed automata using digital clocks
 Proc. Formal Modeling and Analysis of Timed Systems (FORMATS’03), volume 2791 of LNCS
, 2003
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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 53 (15 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.
Probabilistic model checking of the IEEE 802.11 wireless local area network protocol
 Proc. 2nd Joint International Workshop on Process Algebra and Probabilistic Methods, Performance Modeling and Verification (PAPM/PROBMIV’02), volume 2399 of LNCS
, 2002
"... ..."
ModelBased Testing of ObjectOriented Reactive Systems with Spec Explorer
, 2007
"... Testing is one of the costliest aspects of commercial software development. Modelbased testing is a promising approach addressing these deficits. At Microsoft, modelbased testing technology developed by the Foundations of Software Engineering group in Microsoft Research has been used since 2003. T ..."
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Cited by 38 (11 self)
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Testing is one of the costliest aspects of commercial software development. Modelbased testing is a promising approach addressing these deficits. At Microsoft, modelbased testing technology developed by the Foundations of Software Engineering group in Microsoft Research has been used since 2003. The second generation of this tool set, Spec Explorer, deployed in 2004, is now used on a daily basis by Microsoft product groups for testing operating system components,.NET framework components and other areas. This chapter provides a comprehensive survey of the concepts of the tool and their foundations. 1
Symbolic model checking for probabilistic processes using MTBDDs and the Kronecker representation
 In Tools and Algorithms for the Analysis and Construction of Systems, LNCS 1785
, 2000
"... Abstract. This paper reports on experimental results with symbolic model checking of probabilistic processes based on MultiTerminal Binary Decision Diagrams (MTBDDs). We consider concurrent probabilistic systems as models; these allow nondeterministic choice between probability distributions and ar ..."
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Cited by 34 (2 self)
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Abstract. This paper reports on experimental results with symbolic model checking of probabilistic processes based on MultiTerminal Binary Decision Diagrams (MTBDDs). We consider concurrent probabilistic systems as models; these allow nondeterministic choice between probability distributions and are particularly well suited to modelling distributed systems with probabilistic behaviour, e.g. randomized consensus algorithms and probabilistic failures. As a specification formalism we use the probabilistic branchingtime temporal logic PBTL which allows one to express properties such as “under any scheduling of nondeterministic choices, the probability of φ holding until ψ is true is at least 0.78/at most 0.04 ”. We adapt the Kronecker representation of (Plateau 1985), which yields a very compact MTBDD encoding of the system. We implement an experimental model checker using the CUDD package and demonstrate that model construction and reachabilitybased model checking is possible in a matter of seconds for certain classes of systems consisting of up to 10 30 states. 1
Automatic Verification of the IEEE1394 Root Contention Protocol with KRONOS and PRISM
 SOFTWARE TOOLS FOR TECHNOLOGY TRANSFER
"... We report on the automatic verification of timed probabilistic properties of the IEEE 1394 root contention protocol combining two existing tools: the realtime modelchecker Kronos and the probabilistic modelchecker Prism. The system is modelled as a probabilistic timed automaton. We first use Kro ..."
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Cited by 27 (10 self)
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We report on the automatic verification of timed probabilistic properties of the IEEE 1394 root contention protocol combining two existing tools: the realtime modelchecker Kronos and the probabilistic modelchecker Prism. The system is modelled as a probabilistic timed automaton. We first use Kronos to perform a symbolic forward reachability analysis to generate the set of states that are reachable with nonzero probability from the initial state, and before the deadline expires. We then encode this information as a Markov decision process to be analyzed with Prism. We apply this technique to compute the minimal probability of a leader being elected before a deadline, for different deadlines, and study how this minimal probability is influenced by using a biased coin and considering different wire lengths.
Computational Methods for Reachability Analysis of Stochastic Hybrid
 Systems, Hybrid Systems: Computation and Control 2006 LNCS 3927
, 2006
"... Abstract. Stochastic hybrid system models can be used to analyze and design complex embedded systems that operate in the presence of uncertainty and variability. Verification of reachability properties for such systems is a critical problem. Developing algorithms for reachability analysis is challen ..."
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Cited by 25 (8 self)
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Abstract. Stochastic hybrid system models can be used to analyze and design complex embedded systems that operate in the presence of uncertainty and variability. Verification of reachability properties for such systems is a critical problem. Developing algorithms for reachability analysis is challenging because of the interaction between the discrete and continuous stochastic dynamics. In this paper, we propose a probabilistic method for reachability analysis based on discrete approximations. The contribution of the paper is twofold. First, we show that reachability can be characterized as a viscosity solution of a system of coupled HamiltonJacobiBellman equations. Second, we present a numerical method for computing the solution based on discrete approximations and we show that this solution converges to the one for the original system as the discretization becomes finer. Finally, we illustrate the approach with a navigation benchmark that has been proposed for hybrid system verification. 1