Axiomatizing Bisimulation Equivalences and Metrics from Probabilistic SOS Rules

  • Pedro R. D’Argenio
  • Daniel Gebler
  • Matias David Lee
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8412)


Probabilistic transition system specifications (PTSS) provide structural operational semantics for reactive probabilistic labeled transition systems. Bisimulation equivalences and bisimulation metrics are fundamental notions to describe behavioral relations and distances of states, respectively. We provide a method to generate from a PTSS a sound and ground-complete equational axiomatization for strong and convex bisimilarity. The construction is based on the method of Aceto, Bloom and Vaandrager developed for non-deterministic transition system specifications. The novelty in our approach is to employ many-sorted algebras to axiomatize separately non-deterministic choice, probabilistic choice and their interaction. Furthermore, we generalize this method to axiomatize the strong and convex metric bisimulation distance of PTSS.


Normal Form Equational Theory Axiom System Probabilistic Choice Smooth Operator 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Pedro R. D’Argenio
    • 1
  • Daniel Gebler
    • 2
  • Matias David Lee
    • 1
  1. 1.Universidad Nacional de Córdoba & CONICETArgentina
  2. 2.VU University AmsterdamThe Netherlands

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