Comparative Branching-Time Semantics for Markov Chains

Baier, Christel; Hermanns, Holger; Katoen, Joost-Pieter; Wolf, Verena

doi:10.1007/978-3-540-45187-7_32

Cited by 55 publications

(149 citation statements)

References 52 publications

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“…IMCs in which delays are imposed in a compositional manner using the constraint-oriented specification style. The point is that any CTMC can be transformed by a simple linear-time procedure into a weak bisimilar uniform CTMC [3]. Consider the specification P || A D p where P is an IMC with only interactive transitions, i.e., P is an LTS, and D p is a CTMC, probably enhanced with a start action α and end action β as explained before.…”

Section: Definition 11 (Uniform Imc) An Imc Is Uniform If For Any Stmentioning

confidence: 99%

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: Definition 11 (Uniform Imc) An Imc Is Uniform If For Any Stmentioning

confidence: 99%

The How and Why of Interactive Markov Chains

Hermanns

Katoen

2010

Formal Methods for Components and Objects

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“…Now we extend the standard strong [17] and weak bisimulation [4] relations for Markov models to our parametric setting in an obvious way.…”

Section: Bisimulation Relationsmentioning

confidence: 99%

Probabilistic Reachability for Parametric Markov Models

Hahn

Hermanns

Zhang

2009

Model Checking Software

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Abstract. Given a parametric Markov model, we consider the problem of computing the formula expressing the probability of reaching a given set of states. To attack this principal problem, Daws has suggested to first convert the Markov chain into a finite automaton, from which a regular expression is computed. Afterwards, this expression is evaluated to a closed form expression representing the reachability probability. This paper investigates how this idea can be turned into an effective procedure. It turns out that the bottleneck lies in an exponential growth of the regular expression relative to the number of states. We therefore proceed differently, by tightly intertwining the regular expression computation with its evaluation. This allows us to arrive at an effective method that avoids the exponential blow up in most practical cases. We give a detailed account of the approach, also extending to parametric models with rewards and with non-determinism. Experimental evidence is provided, illustrating that our implementation provides meaningful insights on non-trivial models.

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“…Here, we would like to concentrate on equivalences for probabilistic systems. For this class of systems, comparative results have been obtained only for so-called fully probabilistic systems [26,22,2] or only for bisimulation-based and testing-based relations [2,29,35,43].…”

Section: Introductionmentioning

confidence: 99%

Relating strong behavioral equivalences for processes with nondeterminism and probabilities

Bernardo

Nicola

Loreti

2014

Theoretical Computer Science

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We present a comparison of behavioral equivalences for nondeterministic and probabilistic processes whose activities are all observable. In particular, we consider trace-based, testing, and bisimulation-based equivalences. For each of them, we examine the discriminating power of three variants stemming from three approaches that differ for the way probabilities of events are compared when nondeterministic choices are resolved via schedulers. The first approach compares two resolutions with respect to the probability distributions of all considered events. The second approach requires that the probabilities of the set of events of a resolution be individually matched by the probabilities of the same events in possibly different resolutions. The third approach only compares the extremal probabilities of each event stemming from the different resolutions. The three approaches have very reasonable motivations and, when applied to fully nondeterministic processes or fully probabilistic processes, give rise to the classical well studied relations. We shall see that, for processes with nondeterminism and probability, they instead give rise to a much wider variety of behavioral relations, whose discriminating power is thoroughly investigated here in the case of deterministic schedulers.

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Comparative Branching-Time Semantics for Markov Chains

Cited by 55 publications

References 52 publications

The How and Why of Interactive Markov Chains

The How and Why of Interactive Markov Chains

Probabilistic Reachability for Parametric Markov Models

Relating strong behavioral equivalences for processes with nondeterminism and probabilities

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