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Probabilistic Guarded KAT Modulo Bisimilarity: Completeness and Complexity

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arxiv 2305.01755 v1 pith:HVHVTU6D submitted 2023-05-02 cs.LO cs.FL

Wojciech Różowski , Tobias Kappé , Dexter Kozen , Todd Schmid , Alexandra Silva This is my paper · ORCID
classification cs.LOcs.FL
keywords probabilisticbisimilarityprobgkatexpressionsgiveguardedalgebraalgorithm
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abstract

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 $O(n^3 \log n)$ time via a generic partition refinement algorithm.

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