Differential Bisimulation for a Markovian Process Algebra

  • Giulio Iacobelli
  • Mirco Tribastone
  • Andrea Vandin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9234)


Formal languages with semantics based on ordinary differential equations (ODEs) have emerged as a useful tool to reason about large-scale distributed systems. We present differential bisimulation, a behavioral equivalence developed as the ODE counterpart of bisimulations for languages with probabilistic or stochastic semantics. We study it in the context of a Markovian process algebra. Similarly to Markovian bisimulations yielding an aggregated Markov process in the sense of the theory of lumpability, differential bisimulation yields a partition of the ODEs underlying a process algebra term, whereby the sum of the ODE solutions of the same partition block is equal to the solution of a single (lumped) ODE. Differential bisimulation is defined in terms of two symmetries that can be verified only using syntactic checks. This enables the adaptation to a continuous-state semantics of proof techniques and algorithms for finite, discrete-state, labeled transition systems. For instance, we readily obtain a result of compositionality, and provide an efficient partition-refinement algorithm to compute the coarsest ODE aggregation of a model according to differential bisimulation.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Giulio Iacobelli
    • 1
  • Mirco Tribastone
    • 2
  • Andrea Vandin
    • 2
  1. 1.Computing and Systems EngineeringFederal University of Rio de JaneiroRio de JaneiroBrazil
  2. 2.IMT Institute for Advanced Studies LuccaLuccaItaly

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