PEPS: A Package for Solving Complex Markov Models of Parallel Systems

Plateau, Brigitte; Fourneau, Jean-Michel; Lee, Kuei-Hsiang

doi:10.1007/978-1-4613-0533-0_19

Cited by 54 publications

(25 citation statements)

References 9 publications

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“…Then one can avoid having to store the full size matrix by storing the component matrices instead and reformulating steady-state probability calculation in terms of the component matrices. Existing implementation work in this area includes tools such as SMART [11] and PEPS [27].…”

Section: Introductionmentioning

confidence: 99%

Symbolic Model Checking of Probabilistic Processes Using MTBDDs and the Kronecker Representation

Alfaro

Kwiatkowska

Norman

et al. 2000

Tools and Algorithms for the Construction and Analysis of Systems

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Abstract. This paper reports on experimental results with symbolic model checking of probabilistic processes based on Multi-Terminal Binary Decision Diagrams (MTBDDs). We consider concurrent probabilistic systems as models; these allow nondeterministic choice between probability distributions and are particularly well suited to modelling distributed systems with probabilistic behaviour, e.g. randomized consensus algorithms and probabilistic failures. As a specification formalism we use the probabilistic branching-time temporal logic PBTL which allows one to express properties such as "under any scheduling of nondeterministic choices, the probability of φ holding until ψ is true is at least 0.78/at most 0.04 ". We adapt the Kronecker representation of (Plateau 1985), which yields a very compact MTBDD encoding of the system. We implement an experimental model checker using the CUDD package and demonstrate that model construction and reachability-based model checking is possible in a matter of seconds for certain classes of systems consisting of up to 10 30 states.

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Section: Introductionmentioning

confidence: 99%

Symbolic Model Checking of Probabilistic Processes Using MTBDDs and the Kronecker Representation

Alfaro

Kwiatkowska

Norman

et al. 2000

Tools and Algorithms for the Construction and Analysis of Systems

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“…Some popular projection methods are Arnoldi, GMRES, CGS, BiCGSTAB and QMR. Such projections methods can be and have been applied to SANs [1,15,22]. In fact, any iterative or projection method which involves a matrix-vector multiply can be used to ÿnd the stationary distribution of a SAN.…”

Section: Stationary Analysis Of a Sanmentioning

confidence: 99%

The Kronecker product and stochastic automata networks

Langville

2004

Journal of Computational and Applied Mathematics

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This paper can be thought of as a companion paper to Van Loan's The Ubiquitous Kronecker Product paper (J. Comput. Appl. Math. 123 (2000) 85). We collect and catalog the most useful properties of the Kronecker product and present them in one place. We prove several new properties that we discovered in our search for a stochastic automata network preconditioner. We conclude by describing one application of the Kronecker product, omitted from Van Loan's list of applications, namely stochastic automata networks.

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“…The various versions of vector multiplication with a generalized tensor product have been implemented in the software package PEPS, version 3.0 [16]. This version of PEPS is written in C++.…”

Section: Implementation Detailsmentioning

confidence: 99%