Extensional equivalences for transition systems

Nicola, Rocco De

doi:10.1007/bf00264365

Cited by 194 publications

(117 citation statements)

References 15 publications

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“…9. An overview of many other characterizations of unfair mustequivalence for transition systems can be found in [8]. Another approach to fairness is described in [13], where fairness is modelled as a structural property of the operator for parallel composition.…”

Section: Discussionmentioning

confidence: 99%

Fair testing

Brinksma¹,

Rensink

Vogler

1995

CONCUR '95: Concurrency Theory

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Abstract. We investigate the notion of fair testing, a formal testing theory in the style of De Nicola and Hennessy, where divergences are disregarded as long as there axe visible outgoing transitions. The usual testing theories, such as the standard model of failure pre-order, do not allow such fair interpretations because of the way in which they ensure their compositionality with respect to abstraction from observable actions. This feature is usually present in the form of a hiding-operator (CSP, ACP, LOTOS) or part of parallel composition (CCS). Its application can introduce new divergences causing semantic complications. In this paper we present a testing scenario that captures the intended notion of fairness and induces a pre-congruence for abstraction. In the presence of a sufficiently strong synchronisation feature it is shown to be the coarsest pre-congruence contained in the (non-congruent) fair version of failure preorder. We also give a denotational characterisation.

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Section: Discussionmentioning

confidence: 99%

Fair testing

Brinksma¹,

Rensink

Vogler

1995

CONCUR '95: Concurrency Theory

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“…In the case of deterministic schedulers, we shall see that the family of equivalences that assign a central role to schedulers by requiring that the result of a specific choice in one process be fully matched by the other one (fully matching resolutions), yields a hierarchy that is in accordance with the one for fully probabilistic processes in [26,22]. Conversely, the family of equivalences that assign a weaker role to schedulers in resolving nondeterminism (partially matching resolutions), gives rise to relations that are coarser than the previous ones and yields a hierarchy that is in accordance with the one for fully nondeterministic processes in [13,39]. Finally, the family of equivalences that only consider extremal probabilities (max-min-matching resolution sets), has again several analogies with the fully nondeterministic spectrum and yields even coarser relations.…”

Section: Introductionmentioning

confidence: 87%

“…The first study in this direction was presented in [13]. There, most of the then known equivalences over LTS models were "ordered" and it was shown that trace equivalence (equating systems performing the same sequences of actions) is strictly coarser than failure equivalence (equating systems performing the same sequences of actions and refusing the same sets of actions after them), which in turn is strictly coarser than bisimulation equivalence (equating systems performing the same sequences of actions and recursively exhibiting the same behavior).…”

Section: Introductionmentioning

confidence: 99%

“…In our view, the motivations behind the three approaches are all very reasonable. Indeed, when applied to fully nondeterministic processes or fully probabilistic processes, they give rise to well-studied relations that for the fully nondeterministic setting fit into the spectra in [13,39] and for the fully probabilistic setting fit into the spectra in [26,22]. The situation is significantly different when the three approaches are instantiated for nondeterministic and probabilistic processes; in this case, they give rise to a much wider variety of relations.…”

Section: Introductionmentioning

confidence: 99%

“…In Sect. 7, we graphically summarize the results by depicting the spectrum of the considered equivalences, somehow in analogy with the reduced spectrum in [13]. In the same section, additional equivalences are considered and a fuller spectrum, analogous to that in [39], is presented.…”

Section: Introductionmentioning

confidence: 99%

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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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Verification of Specific Properties

Haddad¹,

Vernadat²

2009

Petri Nets

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Extensional equivalences for transition systems

Cited by 194 publications

References 15 publications

Fair testing

Fair testing

Relating strong behavioral equivalences for processes with nondeterminism and probabilities

Verification of Specific Properties

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