Weak Concurrent Kleene Algebra with Application to Algebraic Verification

We propose a generalisation of concurrent Kleene algebra \cite{Hoa09} that can take account of probabilistic effects in the presence of concurrency. The algebra is proved sound with respect to a model of automata modulo a variant of rooted $η$-simulation equivalence. Applicability is demonstrated by algebraic treatments of two examples: algebraic may testing and Rabin's solution to the choice coordination problem.

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