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Symbolic Representations and Analysis of Large State Spaces
 In this Proceedings
, 2003
"... This paper describes symbolic techniques for the construction, representation and analysis of large, probabilistic systems. Symbolic approaches derive their eciency by exploiting highlevel structure and regularity in the models to which they are applied, increasing the size of the state spaces ..."
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Cited by 6 (2 self)
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which can be tackled. In general, this is done by using data structures which provide compact storage but which are still e cient to manipulate, usually based on binary decision diagrams (BDDs) or their extensions. In this paper we focus on BDDs, multivalued decision diagrams (MDDs), multiterminal
Symbolic model checking for probabilistic processes
 IN PROCEEDINGS OF ICALP '97
, 1997
"... We introduce a symbolic model checking procedure for Probabilistic Computation Tree Logic PCTL over labelled Markov chains as models. Model checking for probabilistic logics typically involves solving linear equation systems in order to ascertain the probability of a given formula holding in a stat ..."
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Cited by 97 (29 self)
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state. Our algorithm is based on the idea of representing the matrices used in the linear equation systems by MultiTerminal Binary Decision Diagrams (MTBDDs) introduced in Clarke et al [14]. Our procedure, based on the algorithm used by Hansson and Jonsson [24], uses BDDs to represent formulas
Switching activity analysis for sequential circuits using Boolean approximation method
 in International Symposium on Low Power Electronics and Design
, 1996
"... We propose an incremental probabilistic approach to calculate the signal probabilities and switching activities of the internal nodes of the sequential logic circuits. Spatiotemporal correlations are totally considered by using MultiTerminal Binary Decision Diagrams (MTBDD) with real number valued ..."
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Cited by 1 (0 self)
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We propose an incremental probabilistic approach to calculate the signal probabilities and switching activities of the internal nodes of the sequential logic circuits. Spatiotemporal correlations are totally considered by using MultiTerminal Binary Decision Diagrams (MTBDD) with real number
Leveraging Weighted Automata in Compositional Reasoning about Concurrent Probabilistic Systems
"... We propose the first sound and complete learningbased compositional verification technique for probabilistic safety properties on concurrent systems where each component is an Markov decision process. Different from previous works, weighted assumptions are introduced to attain completeness of ou ..."
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of our framework. Since weighted assumptions can be implicitly represented by multiterminal binary decision diagrams (MTBDD’s), we give an L∗based learning algorithm for MTBDD’s to infer weighted assumptions. Experimental results suggest promising outlooks for our compositional technique.
Symbolic Boolean manipulation with ordered binarydecision diagrams
 ACM COMPUTING SURVEYS
, 1992
"... Ordered BinaryDecision Diagrams (OBDDS) represent Boolean functions as directed acyclic graphs. They form a canonical representation, making testing of functional properties such as satmfiability and equivalence straightforward. A number of operations on Boolean functions can be implemented as grap ..."
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Cited by 1022 (13 self)
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Ordered BinaryDecision Diagrams (OBDDS) represent Boolean functions as directed acyclic graphs. They form a canonical representation, making testing of functional properties such as satmfiability and equivalence straightforward. A number of operations on Boolean functions can be implemented
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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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
An Efficient Representation for Large Arrays of Rational Expressions ∗
, 2010
"... The paper describes a method of representing an ndimensional array of rational expressions as an (n + 1)dimensional array of scalars and shows how this representation readily supports the implementation of various common array operations. A feature of the representation is that it can take advanta ..."
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advantage of memorysaving schemes for encoding large, sparse scalar arrays using multiterminal binary decision diagrams (MTBDDs). The representation involves taking partial fraction expansions of the entries of the array; refining the factorizations of the denominator polynomials as required rather than
On the use of MTBDDs for performability analysis and verification of stochastic systems
"... This paper describes how to employ Multi Terminal Binary Decision Diagrams (MTBDD) for the construction and analysis of a general class of models that exhibit stochastic, probabilistic and nondeterministic behaviour. It is shown how the notorious problem of state space explosion can be circumvented ..."
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Cited by 24 (11 self)
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This paper describes how to employ Multi Terminal Binary Decision Diagrams (MTBDD) for the construction and analysis of a general class of models that exhibit stochastic, probabilistic and nondeterministic behaviour. It is shown how the notorious problem of state space explosion can
asymptotic unavailability with the stochastic process algebra tool CASPAy
, 2010
"... Abstract: CASPA is a stochastic process algebra tool for performance and dependability modelling, analysis, and verification. It is based entirely on the symbolic data structure of the multiterminal binary decision diagram (MTBDD) which enables the tool to handle models with very large state space ..."
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Abstract: CASPA is a stochastic process algebra tool for performance and dependability modelling, analysis, and verification. It is based entirely on the symbolic data structure of the multiterminal binary decision diagram (MTBDD) which enables the tool to handle models with very large state
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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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
Results 11  20
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