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Probabilistic Guarded KAT Modulo Bisimilarity: Completeness and Complexity

Authors Wojciech Różowski , Tobias Kappé , Dexter Kozen , Todd Schmid , Alexandra Silva

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Author Details

Wojciech Różowski
  • Department of Computer Science, University College London, UK
Tobias Kappé
  • Open Universiteit, Heerlen, The Netherlands
  • ILLC, University of Amsterdam, The Netherlands
Dexter Kozen
  • Department of Computer Science, Cornell University, Ithaca, NY, USA
Todd Schmid
  • Department of Computer Science, University College London, UK
Alexandra Silva
  • Department of Computer Science, Cornell University, Ithaca, NY, USA

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Wojciech Różowski, Tobias Kappé, Dexter Kozen, Todd Schmid, and Alexandra Silva. Probabilistic Guarded KAT Modulo Bisimilarity: Completeness and Complexity. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 136:1-136:20, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


We introduce Probabilistic Guarded Kleene Algebra with Tests (ProbGKAT), an extension of GKAT that allows reasoning about uninterpreted imperative programs with probabilistic branching. We give its operational semantics in terms of special class of probabilistic automata. We give a sound and complete Salomaa-style axiomatisation of bisimilarity of ProbGKAT expressions. Finally, we show that bisimilarity of ProbGKAT expressions can be decided in O(n³ log n) time via a generic partition refinement algorithm.

Subject Classification

ACM Subject Classification
  • Theory of computation → Program reasoning
  • Kleene Algebra with Tests
  • program equivalence
  • completeness
  • coalgebra


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