Deciding Bisimilarity and Similarity for Probabilistic Processes

Baier, Christel; Engelen, Bettina; Majster-Cederbaum, Mila

doi:10.1006/jcss.1999.1683

Cited by 114 publications

(178 citation statements)

References 12 publications

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“…simulation preorder or its corresponding equivalence ∩ −1 , but it turns out that checking a simulation relation between probabilistic models such as IMCs is computationally involved [1,67]. In the sequel, we will see that simulation preorders are nonetheless crucial to obtain more aggressive abstraction techniques for IMCs.…”

Section: Theorem 11 For Any Finitely-branching Imc With State Space mentioning

confidence: 99%

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The How and Why of Interactive Markov Chains

Hermanns

Katoen

2010

Formal Methods for Components and Objects

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Abstract. This paper reviews the model of interactive Markov chains (IMCs, for short), an extension of labelled transition systems with exponentially delayed transitions. We show that IMCs are closed under parallel composition and hiding, and show how IMCs can be compositionally aggregated prior to analysis by e.g., bisimulation minimisation or aggressive abstraction based on simulation pre-congruences. We survey some recent analysis techniques for IMCs, i.e., explaining how measures such as reachability probabilities can be obtained. Finally, we demonstrate that IMCs are a natural (and simple) semantic model for stochastic process algebras and generalised stochastic Petri nets and can be used for engineering formalisms such as AADL and dynamic fault trees.

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Section: Theorem 11 For Any Finitely-branching Imc With State Space mentioning

confidence: 99%

“…Accordingly, R(s 0 , s 2 ) = 0.3, E(s 0 ) = 0.3 + 0.6 = 0.9 and P(s 0 , s 2 ) = 1 3 . The probability to move from state s 0 to s 2 within 3 time units is 1 3 · 1 − e −2.7 .…”

Section: Interactive Markov Chainsmentioning

confidence: 99%

The How and Why of Interactive Markov Chains

Hermanns

Katoen

2010

Formal Methods for Components and Objects

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“…Such a definition of ≤ R can be equivalently stated in terms of so-called weight functions between distributions and of maximum flows between networks. In particular, it turns out that d ≤ R e iff the maximum flow of a suitable bipartite network built over the states in supp(d)∪supp(e) and over the relation R is 1 (see [1,13]). …”

Section: Bisimulation and Simulation In Pltssmentioning

confidence: 99%

“…Bisimulation is commonly computed by coarsest partition refinement algorithms [1,8] that iteratively refine a current partition until it becomes the bisimulation partition. Coarsest partition refinements can be cast as shells of partitions: given a property of partitions P ⊆ Part(X), the P-shell of Q ∈ Part(X) corresponds to the coarsest partition refinement of Q that satisfies P, when this exists.…”

Section: Bisimulation As a Shellmentioning

confidence: 99%

“…We show how such a basic procedure can be instantiated to obtain two algorithms that iteratively compute bisimulation and simulation on PLTSs. Interestingly, the standard procedure for computing bisimulations in PLTSs, namely Baier-Engelen-Majster's algorithm [1], can be actually viewed as an implementation of our complete shell procedure that characterizes bisimulation. On the other hand, we show that the corresponding complete shell for computing the simulation preorder yields a new efficient probabilistic simulation algorithm that advances the state-of-theart: in fact, its time and space complexity bounds improve on the best known simulation algorithm for PLTSs by Zhang et al [13].…”

Section: Introductionmentioning

confidence: 99%

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Probabilistic Bisimulation and Simulation Algorithms by Abstract Interpretation

Crafa

Ranzato

2011

Automata, Languages and Programming

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Abstract. We show how bisimulation equivalence and simulation preorder on probabilistic LTSs (PLTSs), namely the main behavioural relations on probabilistic nondeterministic processes, can be characterized by abstract interpretation. Both bisimulation and simulation can be obtained as completions of partitions and preorders, viewed as abstract domains, w.r.t. a pair of concrete functions that encode a PLTS. As a consequence, this approach provides a general framework for designing algorithms for computing bisimulation and simulation on PLTSs. Notably, (i) we show that the standard bisimulation algorithm by Baier et al. can be viewed as an instance of such a framework and (ii) we design a new efficient simulation algorithm that improves the state of the art.

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Partial Order Reduction for Markov Decision Processes: A Survey

Groesser¹,

Baier²

2006

Formal Methods for Components and Objects

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Deciding Bisimilarity and Similarity for Probabilistic Processes

Cited by 114 publications

References 12 publications

The How and Why of Interactive Markov Chains

The How and Why of Interactive Markov Chains

Probabilistic Bisimulation and Simulation Algorithms by Abstract Interpretation

Partial Order Reduction for Markov Decision Processes: A Survey

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