Completeness and Incompleteness of Synchronous Kleene Algebra

  • Jana WagemakerEmail author
  • Marcello Bonsangue
  • Tobias Kappé
  • Jurriaan Rot
  • Alexandra Silva
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11825)


Synchronous Kleene algebra (SKA), an extension of Kleene algebra (KA), was proposed by Prisacariu as a tool for reasoning about programs that may execute synchronously, i.e., in lock-step. We provide a countermodel witnessing that the axioms of SKA are incomplete w.r.t. its language semantics, by exploiting a lack of interaction between the synchronous product operator and the Kleene star. We then propose an alternative set of axioms for SKA, based on Salomaa’s axiomatisation of regular languages, and show that these provide a sound and complete characterisation w.r.t. the original language semantics.



The first author is grateful for discussions with Hans-Dieter Hiep and Benjamin Lion.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Jana Wagemaker
    • 1
    Email author
  • Marcello Bonsangue
    • 2
  • Tobias Kappé
    • 1
  • Jurriaan Rot
    • 1
    • 3
  • Alexandra Silva
    • 1
  1. 1.University College LondonLondonUK
  2. 2.Leiden UniversityLeidenThe Netherlands
  3. 3.Radboud UniversityNijmegenThe Netherlands

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