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OutofCore Solution of Large Linear Systems of Equations Arising from Stochastic Modelling
 In Proc. PAPM/PROBMIV'02, volume 2399 of LNCS
, 2002
"... Many physical or computer systems can be modelled as Markov chains. A range of solution techniques exist to address the statespace explosion problem, encountered while analysing such Markov models. ..."
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Cited by 16 (7 self)
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Many physical or computer systems can be modelled as Markov chains. A range of solution techniques exist to address the statespace explosion problem, encountered while analysing such Markov models.
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.
Deriving Symbolic Representations from Stochastic Process Algebras
, 2002
"... A new denotational semantics for a variant of the stochastic process algebra TIPP is presented, which maps process terms to Multiterminal binary decision diagrams. It is shown that the new semantics is Markovian bisimulation equivalent to the standard SOS semantics. The paper also addresses the ..."
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Cited by 10 (5 self)
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A new denotational semantics for a variant of the stochastic process algebra TIPP is presented, which maps process terms to Multiterminal binary decision diagrams. It is shown that the new semantics is Markovian bisimulation equivalent to the standard SOS semantics. The paper also addresses the difficult question of keeping the underlying state space minimal at every construction step.
Serial Diskbased Analysis of Large Stochastic Models
 In Proc. Dagstuhl Research Seminar
, 2004
"... The paper presents a survey of outofcore methods available for the analysis of large Markov chains on single workstations. First, we discuss the main sparse matrix storage schemes and review iterative methods for the solution of systems of linear equations typically used in diskbased methods. Nex ..."
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Cited by 6 (4 self)
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The paper presents a survey of outofcore methods available for the analysis of large Markov chains on single workstations. First, we discuss the main sparse matrix storage schemes and review iterative methods for the solution of systems of linear equations typically used in diskbased methods. Next, various outofcore approaches for the steady state solution of CTMCs are described. In this context, serial outofcore algorithms are outlined and analysed with the help of their implementations. A comparison of time...
Partiallyshared zerosuppressed multiterminal bdds: concept, algorithms and applications
 Formal Methods in System Design
"... Abstract MultiTerminal Binary Decision Diagrams (MTBDDs) are a well accepted technique for the state graph (SG) based quantitative analysis of large and complex systems specified by means of highlevel model description techniques. However, this type of Decision Diagram (DD) is not always the best ..."
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Cited by 3 (2 self)
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Abstract MultiTerminal Binary Decision Diagrams (MTBDDs) are a well accepted technique for the state graph (SG) based quantitative analysis of large and complex systems specified by means of highlevel model description techniques. However, this type of Decision Diagram (DD) is not always the best choice, since finite functions with small satisfaction sets, and where the fulfilling assignments possess many 0assigned positions, may yield relatively large MTBDD based representations. Therefore, this article introduces zerosuppressed MTBDDs and proves that they are canonical representations of multivalued functions on finite (input) sets. For manipulating DDs of this new type, possibly defined over different sets of function variables, the concept of partiallyshared zerosuppressed MTBDDs and respective algorithms are developed. The efficiency of this new approach is demonstrated by comparing it to the wellknown standard type of MTBDDs, where both types of DDs have been implemented by us within the C++based DDpackage Jinc. The benchmarking takes place in the context of Markovian analysis and probabilistic model checking of systems. In total, the presented work extends existing approaches, since it not only allows one to directly employ (multiterminal) zerosuppressed DDs in the field of quantitative verification, but also clearly demonstrates their efficiency.
Symbolic Composition within the Moebius Framework
 In Proc. of 2’nd MMB Workshop
, 2002
"... This paper describes how to construct complex performability models in the context of the software tool Moebius, by hierarchically composing small submodels. In addition to Moebius' "Join" operator, a second composition operator "Sync" is introduced, and it is shown how b ..."
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Cited by 1 (1 self)
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This paper describes how to construct complex performability models in the context of the software tool Moebius, by hierarchically composing small submodels. In addition to Moebius' "Join" operator, a second composition operator "Sync" is introduced, and it is shown how both types of composition can be realised on the basis of symbolic, i.e. BDDbased data structures.
Implementing the Moebius StateLevel Abstract Functional Interface for ZDDs
"... matrixlayoutindependent numerical solvers be efcient? ..."
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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