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We propose a generalisation of concurrent Kleene algebra \cite{Hoa09} thatcan take account of probabilistic effects in the presence of concurrency. Thealgebra is proved sound with respect to a model of automata modulo a variant ofrooted $\eta$-simulation equivalence. Applicability is demonstrated byalgebraic treatments of two examples: algebraic may testing and Rabin'ssolution to the choice coordination problem.

Weak Concurrent Kleene Algebra with Application to Algebraic Verification