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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 201 (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.
Implementation of Symbolic Model Checking for Probabilistic Systems
, 2002
"... In this thesis, we present ecient implementation techniques for probabilistic model checking, a method which can be used to analyse probabilistic systems such as randomised distributed algorithms, faulttolerant processes and communication networks. A probabilistic model checker inputs a probabilist ..."
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Cited by 70 (21 self)
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In this thesis, we present ecient implementation techniques for probabilistic model checking, a method which can be used to analyse probabilistic systems such as randomised distributed algorithms, faulttolerant processes and communication networks. A probabilistic model checker inputs a probabilistic model and a speci cation, such as \the message will be delivered with probability 1", \the probability of shutdown occurring is at most 0.02" or \the probability of a leader being elected within 5 rounds is at least 0.98", and can automatically verify if the speci cation is true in the model.
Model Checking for Probability and Time: From Theory to Practice
 In Proc. Logic in Computer Science
, 2003
"... Probability features increasingly often in software and hardware systems: it is used in distributed coordination and routing problems, to model faulttolerance and performance, and to provide adaptive resource management strategies. Probabilistic model checking is an automatic procedure for establi ..."
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Cited by 61 (1 self)
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Probability features increasingly often in software and hardware systems: it is used in distributed coordination and routing problems, to model faulttolerance and performance, and to provide adaptive resource management strategies. Probabilistic model checking is an automatic procedure for establishing if a desired property holds in a probabilistic model, aimed at verifying probabilistic specifications such as "leader election is eventually resolved with probability 1", "the chance of shutdown occurring is at most 0.01%", and "the probability that a message will be delivered within 30ms is at least 0.75". A probabilistic model checker calculates the probability of a given temporal logic property being satisfied, as opposed to validity. In contrast to conventional model checkers, which rely on reachability analysis of the underlying transition system graph, probabilistic model checking additionally involves numerical solutions of linear equations and linear programming problems. This paper reports our experience with implementing PRISM (www.cs.bham.ac.uk/dxp/ prism/), a Probabilistic Symbolic Model Checker, demonstrates its usefulness in analysing realworld probabilistic protocols, and outlines future challenges for this research direction.
D.: Symmetry reduction for probabilistic model checking
 International Organization for Standardization. ISO Information Processing Systems  Data Communication HighLevel Data Link Control Procedure  Frame Structure. IS 3309
, 2006
"... Abstract. We present an approach for applying symmetry reduction techniques to probabilistic model checking, a formal verification method for the quantitative analysis of systems with stochastic characteristics. We target systems with a set of nontrivial, but interchangeable, components such as tho ..."
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Cited by 44 (13 self)
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Abstract. We present an approach for applying symmetry reduction techniques to probabilistic model checking, a formal verification method for the quantitative analysis of systems with stochastic characteristics. We target systems with a set of nontrivial, but interchangeable, components such as those which commonly arise in randomised distributed algorithms or probabilistic communication protocols. We show, for three types of probabilistic models, that symmetry reduction, similarly to the nonprobabilistic case, allows verification to instead be performed on a bisimilar quotient model which may be up to factorially smaller. We then propose an efficient algorithm for the construction of the quotient model using a symbolic implementation based on multiterminal binary decision diagrams (MTBDDs) and, using four large case studies, demonstrate that this approach offers not only a dramatic increase in the size of probabilistic model which can be quantitatively analysed but also a significant decrease in the corresponding runtimes. 1
2007): Bisimulation Minimisation Mostly Speeds Up Probabilistic Model Checking
 In: Tools and Algorithms for the Construction and Analysis of Systems, 13th International Conference (TACAS’07), Lecture Notes in Computer Science 4424
"... The following full text is a publisher's version. ..."
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Cited by 37 (9 self)
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The following full text is a publisher's version.
A Symbolic OutofCore Solution Method for Markov Models
 In Proc. Workshop on Parallel and Distributed Model Checking (PDMC'02), volume 68.4 of Electronic Notes in Theoretical Computer Science
, 2002
"... Despite considerable eort, the statespace explosion problem remains an issue in the analysis of Markov models. Given structure, symbolic representations can result in very compact encoding of the models. However, a major obstacle for symbolic methods is the need to store the probability vector(s) e ..."
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Cited by 14 (11 self)
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Despite considerable eort, the statespace explosion problem remains an issue in the analysis of Markov models. Given structure, symbolic representations can result in very compact encoding of the models. However, a major obstacle for symbolic methods is the need to store the probability vector(s) explicitly in main memory. In this paper, we present a novel algorithm which relaxes these memory limitations by storing the probability vector on disk. The algorithm has been implemented using an MTBDDbased data structure to store the matrix and an array to store the vector. We report on experimental results for two benchmark models, a Kanban manufacturing system and a exible manufacturing system, with models as large as 133 million states.
Advances in Model Representations
 Proc. PAPM/PROBMIV 2001, Available as Volume 2165 of LNCS (2001
, 2001
"... We review highlevel specification formalisms for Markovian performability models, thereby emphasising the role of structuring concepts as realised par excellence by stochastic process algebras. Symbolic representations based on decision diagrams are presented, and it is shown that they quite id ..."
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Cited by 9 (4 self)
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We review highlevel specification formalisms for Markovian performability models, thereby emphasising the role of structuring concepts as realised par excellence by stochastic process algebras. Symbolic representations based on decision diagrams are presented, and it is shown that they quite ideally support compositional model construction and analysis.
Symbolic Performance and Dependability Evaluation with the Tool CASPA
 In FORTE Workshops, volume 3236 of LNCS
, 2004
"... This paper describes the tool CASPA,anewperformance evaluation tool which is based on a Markovian stochastic process algebra. ..."
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Cited by 8 (2 self)
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This paper describes the tool CASPA,anewperformance evaluation tool which is based on a Markovian stochastic process algebra.
Implicit GSPN reachability set generation using decision diagrams. Performance Evaluation
 Perf. Eval
, 2004
"... Implicit techniques for representing and generating the reachability set of a highlevel model have become quite efficient. However, such techniques are usually restricted to models whose events have equal priority. Models containing events with differing classes of priority or complex priority stru ..."
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Cited by 6 (2 self)
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Implicit techniques for representing and generating the reachability set of a highlevel model have become quite efficient. However, such techniques are usually restricted to models whose events have equal priority. Models containing events with differing classes of priority or complex priority structure, in particular models with immediate events, have thus been required to use lessefficient explicit reachability set generation techniques. In this paper, we present an efficient implicit technique, based on multivalued decision diagram representations for sets of states and matrix diagram representations for nextstate functions, that can handle models with complex priority structure. We adapt an efficient Kroneckerbased reachability set generation algorithm to work with matrix diagrams. If the model contains immediate events, the vanishing states can be eliminated either during generation, by manipulating the matrix diagram, or after generation, by manipulating the multivalued decision diagram. We apply both techniques to several models and give detailed experimental results. 1.