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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.
Symbolic Representations and Analysis of Large Probabilistic Systems
 In Validation of Stochastic Systems
, 2004
"... Abstract. This paper describes symbolic techniques for the construction, representation and analysis of large, probabilistic systems. Symbolic approaches derive their efficiency by exploiting highlevel structure and regularity in the models to which they are applied, increasing the size of the stat ..."
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Cited by 18 (2 self)
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Abstract. This paper describes symbolic techniques for the construction, representation and analysis of large, probabilistic systems. Symbolic approaches derive their efficiency by exploiting highlevel structure and regularity in the models to which they are applied, increasing the size of the state spaces which can be tackled. In general, this is done by using data structures which provide compact storage but which are still efficient to manipulate, usually based on binary decision diagrams (BDDs) or their extensions. In this paper we focus on BDDs, multivalued decision diagrams (MDDs), multiterminal binary decision diagrams (MTBDDs) and matrix diagrams. 1
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.
Symbolic Reachability for Process Algebras with Recursive Data Types
 University of Twente
, 2008
"... Abstract. In this paper, we present a symbolic reachability algorithm for process algebras with recursive data types. Like the various saturation based algorithms of Ciardo et al, the algorithm is based on partitioning of the transition relation into events whose influence is local. As new features ..."
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Abstract. In this paper, we present a symbolic reachability algorithm for process algebras with recursive data types. Like the various saturation based algorithms of Ciardo et al, the algorithm is based on partitioning of the transition relation into events whose influence is local. As new features, our algorithm supports recursive data types and allows unbounded nondeterminism, which is needed to support open systems with data. The algorithm does not use any specific features of process algebras. That is, it will work for any system that consists of a fixed number of communicating processes, where in each atomic step only a subset of the processes participate. As proof of concept we have implemented the algorithm in the context of the µCRL toolset. We also compared the performance of this prototype with the performance of the existing explicit tools on a set of typical case studies. 1
Symbolic Model Checking of Stochastic Systems: Theory and Implementation
"... Abstract. This paper presents IMSPDL, a stochastic extension of the modal logic PDL, which supports the specification of complex performance and dependability requirements. The logic is interpreted over extended stochastic labelled transition systems (ESLTS), i.e. transition systems containing both ..."
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Abstract. This paper presents IMSPDL, a stochastic extension of the modal logic PDL, which supports the specification of complex performance and dependability requirements. The logic is interpreted over extended stochastic labelled transition systems (ESLTS), i.e. transition systems containing both immediate and Markovian transitions. We define the syntax and semantics of the new logic and show that IMSPDL provides powerful means to specify pathbased properties with timing restrictions. In general, paths can be characterised by regular expressions, also called programs, where the executability of a program may depend on the validity of test formulae. For the model checking of IMSPDL timebounded path formulae, a deterministic program automaton is constructed from the requirement. Afterwards the product transition system between this automaton and the ESLTS is built and subsequently transformed into a continuous time Markov Chain (CTMC) on which numerical analysis is performed. Empirical results given in the paper show that model checking IMSPDL can be realised efficiently in practice.
Activitylocal symbolic state graph generation for highlevel stochastic models
 In Proceedings of the 13th GI/ITG Conference on Measurement, Modeling, and Evaluation of Computer and Communication Systems (MMB
, 2006
"... Abstract. This paper introduces a new, efficient method for deriving compact symbolic representations of very large (labelled) Markov chains resulting from highlevel model specifications such as stochastic Petri nets, stochastic process algebras, etc.. This so called “activitylocal” scheme is comb ..."
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Cited by 4 (2 self)
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Abstract. This paper introduces a new, efficient method for deriving compact symbolic representations of very large (labelled) Markov chains resulting from highlevel model specifications such as stochastic Petri nets, stochastic process algebras, etc.. This so called “activitylocal” scheme is combined with a new data structure, called zerosuppressed multiterminal binary decision diagram, and a new efficient “activityoriented” scheme for symbolic reachability analysis. Several standard benchmark models from the literature are analyzed in order to show the superiority of our approach. 1
SPDL Model Checking via PropertyDriven State Space Generation
"... Abstract. In this report we describe how both, memory and time requirements for stochastic model checking of SPDL (stochastic propositional dynamic logic) formulae can significantly be reduced. SPDL is the stochastic extension of the multimodal program logic PDL. SPDL provides means to specify pa ..."
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Abstract. In this report we describe how both, memory and time requirements for stochastic model checking of SPDL (stochastic propositional dynamic logic) formulae can significantly be reduced. SPDL is the stochastic extension of the multimodal program logic PDL. SPDL provides means to specify pathbased properties with or without timing restrictions. Paths can be characterised by socalled programs, essentially regular expressions, where the executability can be made dependent on the validity of test formulae. For modelchecking SPDL path formulae it is necessary to build a product transition system (PTS) between the system model and the program automaton belonging to the path formula that is to be verified. In many cases, this PTS can be drastically reduced during the model checking procedure, as the program restricts the number of potentially satisfying paths. Therefore, we propose an approach that directly generates the reduced PTS from a given SPA specification and an SPDL path formula. The feasibility of this approach is shown through a selection of case studies, which show enormous state space reductions, at no increase in generation time. 1
CASPA: A Tool for Symbolic Performance and Dependability Evaluation
"... Symbolic data structures, such as binary decision diagrams (BDD) [1] and variants thereof have proved to be suitable for the efficient generation and compact representation of very large state spaces and transition systems. The key to such ..."
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Symbolic data structures, such as binary decision diagrams (BDD) [1] and variants thereof have proved to be suitable for the efficient generation and compact representation of very large state spaces and transition systems. The key to such
Scalable Stochastic Modelling for Resilience
"... Abstract. This chapter summarises techniques that are suitable for performance and resilience modelling and analysis of massive stochastic systems. We will introduce scalable techniques that can be applied to models constructed using DTMCs and CTMCs as well as compositional formalisms such as stocha ..."
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Abstract. This chapter summarises techniques that are suitable for performance and resilience modelling and analysis of massive stochastic systems. We will introduce scalable techniques that can be applied to models constructed using DTMCs and CTMCs as well as compositional formalisms such as stochastic automata networks, stochastic process algebras and queueing networks. We will briefly show how techniques such as mean value analysis, meanfield analysis, symbolic data structures and fluid analysis can be used to analyse massive models specifically for resilience in networks, communication and computer architectures. 1