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FoSSaCS 2012: Foundations of Software Science and Computational Structures pp 195–209Cite as

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Revisiting Trace and Testing Equivalences for Nondeterministic and Probabilistic Processes

Revisiting Trace and Testing Equivalences for Nondeterministic and Probabilistic Processes

  • Marco Bernardo17,
  • Rocco De Nicola18 &
  • Michele Loreti19 
  • Conference paper
  • 884 Accesses

  • 4 Citations

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 7213)

Abstract

One of the most studied extensions of testing theory to nondeterministic and probabilistic processes yields unrealistic probabilities estimations that give rise to two anomalies. First, probabilistic testing equivalence does not imply probabilistic trace equivalence. Second, probabilistic testing equivalence differentiates processes that perform the same sequence of actions with the same probability but make internal choices in different moments and thus, when applied to processes without probabilities, does not coincide with classical testing equivalence. In this paper, new versions of probabilistic trace and testing equivalences are presented for nondeterministic and probabilistic processes that resolve the two anomalies. Instead of focussing only on suprema and infima of the set of success probabilities of resolutions of interaction systems, our testing equivalence matches all the resolutions on the basis of the success probabilities of their identically labeled computations. A simple spectrum is provided to relate the new relations with existing ones. It is also shown that, with our approach, the standard probabilistic testing equivalences for generative and reactive probabilistic processes can be retrieved.

Keywords

  • Probabilistic Failure
  • Success Probability
  • Test Equivalence
  • Probabilistic Choice
  • Label Transition System

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Work partially supported by the FP7-IST-FET Project ASCENS, grant n. 257414.

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Author information

Authors and Affiliations

  1. Dipartimento di Scienze di Base e Fondamenti, Università di Urbino, Italy

    Marco Bernardo

  2. IMT, Istituto Alti Studi Lucca, Italy

    Rocco De Nicola

  3. Dipartimento di Sistemi e Informatica, Università di Firenze, Italy

    Michele Loreti

Authors
  1. Marco Bernardo
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  2. Rocco De Nicola
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  3. Michele Loreti
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Editor information

Editors and Affiliations

  1. IT University of Copenhagen, Rued Langgaards Vej 7, 2300, Copenhagen, Denmark

    Lars Birkedal

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© 2012 Springer-Verlag Berlin Heidelberg

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Bernardo, M., De Nicola, R., Loreti, M. (2012). Revisiting Trace and Testing Equivalences for Nondeterministic and Probabilistic Processes. In: Birkedal, L. (eds) Foundations of Software Science and Computational Structures. FoSSaCS 2012. Lecture Notes in Computer Science, vol 7213. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28729-9_13

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  • DOI: https://doi.org/10.1007/978-3-642-28729-9_13

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  • Print ISBN: 978-3-642-28728-2

  • Online ISBN: 978-3-642-28729-9

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