Revisiting Trace and Testing Equivalences for Nondeterministic and Probabilistic Processes

  • Marco Bernardo
  • Rocco De Nicola
  • Michele Loreti
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7213)


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.


Probabilistic Failure Success Probability Test Equivalence Probabilistic Choice Label Transition System 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Marco Bernardo
    • 1
  • Rocco De Nicola
    • 2
  • Michele Loreti
    • 3
  1. 1.Dipartimento di Scienze di Base e FondamentiUniversità di UrbinoItaly
  2. 2.IMTIstituto Alti Studi LuccaItaly
  3. 3.Dipartimento di Sistemi e InformaticaUniversità di FirenzeItaly

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