Testing Preorders for Probabilistic Processes

Cleaveland, Rance; Dayar, Zeynep; Smolka, Scott A.; Yuen, Shoji

doi:10.1006/inco.1999.2808

Cited by 68 publications

(55 citation statements)

References 4 publications

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“…In contrast, the interaction system of the first process and the test results in four maximal resolutions in which success is respectively reached with probability 1, p 1 , p 2 , and 0. Likewise, ∼ PTe-and ∼ PTe-∀∃ are not backward compatible with the testing equivalence defined in [10] for fully probabilistic processes (see the full version of [4] for a counterexample).…”

Section: Definition 51 a Nondeterministic And Probabilistic Test Nmentioning

confidence: 99%

“…While ∼ PTe-, ∼ PTe-∀∃ , and ∼ PTe-tbt,dis are not conservative extensions of the testing equivalence defined in [14] for fully nondeterministic processes -which we denote by ∼ Te,fnd -and the testing equivalence defined in [10] for fully probabilistic processes -which we denote by ∼ Te,fpr -the other two testing equivalences are backward compatible with them.…”

Section: Definition 51 a Nondeterministic And Probabilistic Test Nmentioning

confidence: 99%

“…Moreover, the resulting probabilistic testing equivalence is neither a conservative extension of testing equivalence for fully nondeterministic processes [14] nor a conservative extension of testing equivalence for fully probabilistic processes [10]. 3.…”

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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Section: Definition 51 a Nondeterministic And Probabilistic Test Nmentioning

confidence: 99%

Section: Definition 51 a Nondeterministic And Probabilistic Test Nmentioning

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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“…In terms of other related work, there is significant work on testing preorders and equivalences for probabilistic processes [4,16,19,5,3,20,14,13]. Most of these proposals follow the de Nicola and Hennessy's style [6,9], that is, two processes are equivalent if the application of any test belonging to a given set returns the same result.…”

Section: Introductionmentioning

confidence: 99%

Derivation of a Suitable Finite Test Suite for Customized Probabilistic Systems

Llana-Díaz

Núñez

Rodrı́guez

2006

Lecture Notes in Computer Science

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Abstract. In order to check the conformance of an IUT (implementation under test) with respect to a specification, it is not feasible, in general, to test the whole set of IUT available behaviors. In some situations, testing the behavior of the IUT assuming that it is stimulated by a given usage model is more appropriate. Specifically, if we consider that specifications and usage models are defined in probabilistic terms, then by applying a finite set of tests to the IUT we can compute a relevant metric: An upper bound of the probability that a user following the usage model finds an error in the IUT. We also present a method to find an optimal (with respect to the number of inputs) set of tests that minimizes that upper bound.

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“…In section 4, we give a formal language for the specification of trace properties, including those formulated using Büchi or Rabin automata. In section 5, we explain how to analyze those properties backward and in section 6.1 how to apply abstract analyses. Appendices give mathematical background and necessary lemmas on measure theory, the Lebesgue integral, and lattice theory.…”

mentioning

confidence: 99%

Abstract Interpretation of Programs as Markov Decision Processes

Monniaux

2003

Static Analysis

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Testing Preorders for Probabilistic Processes

Cited by 68 publications

References 4 publications

Relating strong behavioral equivalences for processes with nondeterminism and probabilities

Relating strong behavioral equivalences for processes with nondeterminism and probabilities

Derivation of a Suitable Finite Test Suite for Customized Probabilistic Systems

Abstract Interpretation of Programs as Markov Decision Processes

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