Formalisation of Probabilistic Testing Semantics in Coq

  • Yuxin DengEmail author
  • Jean-Francois Monin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11760)


Van Breugel et al. [Theor. Comput. Sci. 333(1–2):171–197, 2005] have given an elegant testing framework that can characterise probabilistic bisimulation, but its completeness proof is highly involved. Deng and Feng [Inf. Comput. 257:58–64, 2017] have simplified that result for finite-state processes. The crucial part in the latter work is an algorithm that can construct enhanced tests. We formalise the algorithm and prove its correctness by maintaining a number of subtle invariants in Coq. To support the formalisation, we develop a reusable library for manipulating finite sets. This sets an early example of formalising probabilistic concurrency theory or quantitative aspects of concurrency theory at large, which is a rich field to be pursued.



We would like to thank Yves Bertot for helpful discussion.


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Authors and Affiliations

  1. 1.Shanghai Key Laboratory of Trustworthy ComputingMOE International Joint Lab of Trustworthy Software, East China Normal UniversityShanghaiChina
  2. 2.Univ. Grenoble Alpes, CNRS, Grenoble INP, VERIMAGGrenobleFrance

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