Trace Machines for Observing Continuous-Time Markov Chains

Wolf, Verena; Baier, Christel; Majster-Cederbaum, Mila

doi:10.1016/j.entcs.2005.10.042

Cited by 19 publications

(20 citation statements)

References 6 publications

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“…As far as quantitative notions of equivalence relations are concerned, in the last 20 years several different semantics have been considered, as also witnessed in the context of QAPL, which in such a sense proposes interesting representatives of the lines of research in this field. Such studies include linear-time equivalences, like trace equivalence for continuous-time Markov chains [145] and for interactive Markov chains [146]; probabilistic barbed congruence [57], which coincides with observational equivalence for a version of CCS including a probabilistic guarded choice operator, branching bisimulation congruence for probabilistic transition systems obeying a general alternating model of probabilistic and nondeterministic states [11] and for a more general probabilistic transition system specification format [104], weak bisimulation for continuous-time Markov chains [23] and for Markov automata [6]; testing equivalence for reactive probabilistic processes [71] and for nondeterministic, probabilistic, and Markovian processes [22], reward-based testing preorders for probabilistic labeled transition systems [59]; finally, a spectrum of different probabilistic equivalences, including trace, bisimulation, and testing semantics, in the setting of nondeterministic and probabilistic processes [24], a generalized notion of bisimulation for state-to-function transition systems that is comparable to many other quantitative notions of bisimulation [103], and undecidability results of bisimulation on Petri nets under durational semantics [100].…”

Section: Information Flow Analysis and Equivalence Checkingmentioning

confidence: 99%

Quantitative Aspects of Programming Languages and Systems over the past 2^4 years and beyond

Aldini

2020

Electron. Proc. Theor. Comput. Sci.

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Quantitative aspects of computation are related to the use of both physical and mathematical quantities, including time, performance metrics, probability, and measures for reliability and security. They are essential in characterizing the behaviour of many critical systems and in estimating their properties. Hence, they need to be integrated both at the level of system modeling and within the verification methodologies and tools. Along the last two decades a variety of theoretical achievements and automated techniques have contributed to make quantitative modeling and verification mainstream in the research community. In the same period, they represented the central theme of the series of workshops entitled Quantitative Aspects of Programming Languages and Systems (QAPL) and born in 2001. The aim of this survey is to revisit such achievements and results from the standpoint of QAPL and its community.

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Section: Information Flow Analysis and Equivalence Checkingmentioning

confidence: 99%

Quantitative Aspects of Programming Languages and Systems over the past 2^4 years and beyond

Aldini

2020

Electron. Proc. Theor. Comput. Sci.

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“…In this section we recall the non-deterministic, probabilistic and Markovian versions of trace equivalence, which were originally defined in Hoare (1985), Jou and Smolka (1990) and Wolf et al (2005). Instead, we consider directly the finite-length computations of the process terms taken in isolation, thus abstracting from the branching points of their behaviour.…”

Section: Trace Equivalencementioning

confidence: 99%

A survey of modal logics characterising behavioural equivalences for non-deterministic and stochastic systems

Bernardo

Botta

2008

Math. Struct. Comp. Sci.

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Link to this article: http://journals.cambridge.org/abstract_S0960129507006408How to cite this article: MARCO BERNARDO and STEFANIA BOTTA (2008). A survey of modal logics characterising behavioural equivalences for non-deterministic and stochastic systems.Behavioural equivalences are a means of establishing whether computing systems possess the same properties. The specific set of properties that are preserved by a specific behavioural equivalence clearly depends on how the system behaviour is observed and can usually be characterised by means of a modal logic. In this paper we consider three different approaches to the definition of behavioural equivalences -bisimulation, testing and traceapplied to three different classes of systems -non-deterministic, probabilistic and Markovian -and we survey the nine resulting modal logic characterisations, each of which stems from the Hennessy-Milner logic. We then compare the nine characterisations with respect to the logical operators, in order to emphasise the differences between the three approaches in the definition of behavioural equivalences and the regularities within each of them. In the probabilistic and Markovian cases we also address the issue of whether the probabilistic and temporal aspects should be treated in a local or global way and consequently whether the modal logic interpretation should be qualitative or quantitative.

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“…Markovian trace equivalence [8] considers two process terms to be equivalent whenever they are able to execute computations with the same functional and performance characteristics. It relies on comparing the process term probabilities of performing a computation within a given sequence of average amounts of time.…”

Section: Markovian Trace Equivalencementioning

confidence: 99%

“…Instead, Markovian testing equivalence [1] considers two models to be equivalent whenever an external observer interacting with them by means of tests is not able to distinguish between them from the functional or performance viewpoint. Finally, Markovian trace equivalence [8] considers two models to be equivalent whenever they are able to execute computations with the same functional and performance characteristics.…”

Section: Introductionmentioning

confidence: 99%

Towards State Space Reduction Based on T-Lumpability-Consistent Relations

Bernardo

2008

Computer Performance Engineering

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Abstract. Markovian behavioral equivalences can be exploited for state space reduction before performance evaluation takes place. It is known that Markovian bisimilarity corresponds to ordinary lumpability and that Markovian testing and trace equivalences correspond to a coarser exact relation we call T-lumpability. While there exists an ordinarylumpability-consistent aggregation algorithm, this is not the case with T-lumpability. Based on the axiomatization of Markovian testing and trace equivalences, we provide a sufficient condition for T-lumpability that can easily be embedded in the aggregation algorithm for ordinary lumpability, thus enhancing the potential for exact state space reduction. We also identify a class of systems -those providing incremental services -for which the resulting aggregation algorithm turns out to be useful.

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Trace Machines for Observing Continuous-Time Markov Chains

Cited by 19 publications

References 6 publications

Quantitative Aspects of Programming Languages and Systems over the past 2^4 years and beyond

Quantitative Aspects of Programming Languages and Systems over the past 2^4 years and beyond

A survey of modal logics characterising behavioural equivalences for non-deterministic and stochastic systems

Towards State Space Reduction Based on T-Lumpability-Consistent Relations

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