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32
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.
The Möbius Framework and Its Implementation
"... The Möbius framework is an environment for supporting multiple modeling formalisms and solution techniques. Models expressed in formalisms that are compatible with the framework are translated into equivalent models using Mobius framework components. This translation preserves the structure of the m ..."
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Cited by 113 (21 self)
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The Möbius framework is an environment for supporting multiple modeling formalisms and solution techniques. Models expressed in formalisms that are compatible with the framework are translated into equivalent models using Mobius framework components. This translation preserves the structure of the models, allowing e#cient solutions. The framework is implemented in the tool by a welldefined abstract functional interface. Models and solution techniques interact with one another through the use of the standard interface, allowing them to interact with Mobius framework components, not formalism components. This permits novel combinations of modeling techniques, and will be a catalyst for new research in modeling techniques. This paper describes our approach, focusing on the "atomic model." We describe the formal description of the Mobius components as well as their implementations in our software tool.
Complexity of memoryefficient Kronecker operations with applications to the solution of Markov models
 INFORMS J. Comp
, 2000
"... We present new algorithms for the solution of large structured Markov models whose infinitesimal generator can be expressed as a Kronecker expression of sparse matrices. We then compare them with the shufflebased method commonly used in this context and show how our new algorithms can be advantageo ..."
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Cited by 69 (20 self)
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We present new algorithms for the solution of large structured Markov models whose infinitesimal generator can be expressed as a Kronecker expression of sparse matrices. We then compare them with the shufflebased method commonly used in this context and show how our new algorithms can be advantageous in dealing with very sparse matrices and in supporting both Jacobistyle and GaussSeidelstyle methods with appropriate multiplication algorithms. Our main contribution is to show how solution algorithms based on Kronecker expression can be modified to consider probability vectors of size equal to the "actual" state space instead of the "potential" state space, thus providing space and time savings. The complexity of our algorithms is compared under different sparsity assumptions. A nontrivial example is studied to illustrate the complexity of the implemented algorithms. Continuous time Markov chains (CTMCs) are an established technique to analyze the performance, reliability, or performability of dynamic systems from a wide range of application areas. CTMCs are usually specied in a highlevel modeling formalism, then a software tool is employed to generate the state space and generator matrix of the underlying CTMC and compute the stationary
Symbolic Statespace Exploration and Numerical Analysis of Statesharing Composed Models
 IN PROCEEDINGS OF NSMC ’03: THE FOURTH INTERNATIONAL CONFERENCE ON THE NUMERICAL SOLUTION OF MARKOV CHAINS
, 2004
"... The complexity of stochastic models of realworld systems is usually managed by abstracting details and structuring models in a hierarchical manner. Systems are often built by replicating and joining subsystems, making possible the creation of a model structure that yields lumpable state spaces. Thi ..."
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Cited by 18 (6 self)
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The complexity of stochastic models of realworld systems is usually managed by abstracting details and structuring models in a hierarchical manner. Systems are often built by replicating and joining subsystems, making possible the creation of a model structure that yields lumpable state spaces. This fact has been exploited to facilitate modelbased numerical analysis. Likewise, recent results on model construction suggest that decision diagrams can be used to compactly represent large Continuous Time Markov Chains (CTMCs). In this paper, we present an approach that combines and extends these two approaches. In particular, we propose methods that apply to hierarchically structured models with hierarchies based on sharing state variables. The hierarchy is constructed in a way that exposes structural symmetries in the constructed model, thus facilitating lumping. In addition, the methods allow one to derive a symbolic representation of the associated CTMC directly from the given model without the need to compute and store the overall state space or CTMC explicitly. The resulting representation of a generator matrix allows the analysis of large CTMCs in lumped form. The efficiency of the approach is demonstrated with the help of two example models.
A Structured PathBased Approach for Computing Transient Rewards of Large CTMCs
"... Structured (a.k.a. symbolic) representation techniques of Markov models have, to a large extent, been used effectively for representing very large transition matrices and their associated state spaces. However, their success means that the largest space requirement encountered when analyzing these m ..."
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Cited by 16 (7 self)
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Structured (a.k.a. symbolic) representation techniques of Markov models have, to a large extent, been used effectively for representing very large transition matrices and their associated state spaces. However, their success means that the largest space requirement encountered when analyzing these models is often the representation of their iteration and solution vectors. In this paper, we present a new approach for computing bounds on solutions of transient measures in large continuoustime Markov chains (CTMCs). The approach extends existing path and uniformizationbased methods by identifying sets of paths that are equivalent with respect to a reward measure and related to one another via a simple structural relationship. This relationship allows us to explore multiple paths at the same time, thus significantly increasing the number of paths that can be explored in a given amount of time. Furthermore, the use of a structured representation for the state space and the direct computation of the desired reward measure (without ever storing the solution vector) allow us to analyze very large models using a very small amount of storage. In addition to presenting the method itself, we illustrate its use to compute the reliability and the availability of a large distributed information service system in which faults may propagate across subsystems.
Möbius: Framework and Atomic Models
, 2001
"... This paper gives an overview of the M obius framework, and gives a formal specification for defining atomic models within the framework. The framework is designed to be capable of incorporating multiple modeling formalisms, including atomic models (e.g, SPNs), composition formalisms (e.g., Replicate ..."
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Cited by 14 (5 self)
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This paper gives an overview of the M obius framework, and gives a formal specification for defining atomic models within the framework. The framework is designed to be capable of incorporating multiple modeling formalisms, including atomic models (e.g, SPNs), composition formalisms (e.g., Replicate/Join), measure specification formalisms, connection formalisms, and solvers. We focus on atomic models, which are composed of actions, state variables, and properties. We argue that these are sufficient to specify a large number of atomic model formalisms in the M obius framework. The framework serves as a basis for the M obius tool [13].
On Automated Verification of Probabilistic Programs
, 2007
"... We introduce a simple procedural probabilistic programming language which is suitable for coding a wide variety of randomised algorithms and protocols. This language is interpreted over nite datatypes and has a decidable equivalence problem. We have implemented an automated equivalence checker, whic ..."
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Cited by 14 (7 self)
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We introduce a simple procedural probabilistic programming language which is suitable for coding a wide variety of randomised algorithms and protocols. This language is interpreted over nite datatypes and has a decidable equivalence problem. We have implemented an automated equivalence checker, which we call apex, for this language, based on game semantics. We illustrate our approach with three nontrivial case studies: (i) Herman's selfstabilisation algorithm; (ii) an analysis of the average shape of binary search trees obtained by certain sequences of random insertions and deletions; and (iii) the problem of anonymity in the Dining Cryptographers protocol. In particular, we record an exponential speedup in the latter over stateoftheart competing approaches.
Traviando  Debugging Simulation Traces with Message Sequence Charts
 IN INTERNATIONAL CONFERENCE ON QUANTITATIVE EVALUATION OF SYSTEMS (QEST
, 2006
"... Discrete event simulation is broadly applied in the analysis of dynamic and concurrent systems and often with complex and detailed models. The process of creation and coding a nontrivial simulation model is error prone and the identification and understanding of what really goes on in a simulati ..."
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Cited by 9 (5 self)
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Discrete event simulation is broadly applied in the analysis of dynamic and concurrent systems and often with complex and detailed models. The process of creation and coding a nontrivial simulation model is error prone and the identification and understanding of what really goes on in a simulation run needs adequate tool support for makeing verification, validation and debugging productive. This holds in particular for the analysis of simulation traces, a powerfull debugging aid with the challenge of large amounts of data. In this paper, we present Traviando, a Trace Visualizer and Analyzer from Dortmund university.
Integrating synchronization with priority into a Kronecker representation, in:
 Proceedings of the 11th International Conference on TOOLS2000,
, 2000
"... Abstract The compositional representation of a Markov chain using Kronecker algebra, according to a compositional model representation as a superposed generalized stochastic Petri net or a stochastic automata network, has been studied for a while. In this paper we describe a Kronecker expression an ..."
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Cited by 6 (2 self)
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Abstract The compositional representation of a Markov chain using Kronecker algebra, according to a compositional model representation as a superposed generalized stochastic Petri net or a stochastic automata network, has been studied for a while. In this paper we describe a Kronecker expression and associated data structures, that allows to handle nets with synchronization over activities of different levels of priority. New algorithms for these structures are provided to perform an iterative solution method of Jacobi or GaussSeidel type. These algorithms are implemented in the APNN Toolbox. We use this implementation in combination with GreatSPN and exercise an example that illustrates characteristics of the presented algorithms.
Möbius 2.3: An Extensible Tool for Dependability, Security, and Performance Evaluation of Large and Complex System Models
"... Möbius 2.3 is an extensible dependability, security, and performance modeling environment for largescale discreteevent systems. It provides multiple model formalisms and solution techniques, facilitating the representation of each part of a system in the formalism that is most appropriate for it, ..."
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Cited by 6 (0 self)
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Möbius 2.3 is an extensible dependability, security, and performance modeling environment for largescale discreteevent systems. It provides multiple model formalisms and solution techniques, facilitating the representation of each part of a system in the formalism that is most appropriate for it, and the application of the solution method or methods bestsuited to estimating the system’s behavior. Since its initial release in 2001, many advances have been made in Möbius’ design and implementation that have strengthened its place in the modeling and analysis community. With almost a decade of widespread academic and industrial use, Möbius has proven itself to be useful in a wide variety of modeling situations. This paper documents the current feature set of Möbius 2.3, emphasizing recent significant enhancements.