Probabilistic Kleene Algebra with Angelic Nondeterminism
Shawn Ong, Stephanie Ma, Dexter C. Kozen · Proceedings of the ACM on Programming Languages · 2025
We introduce a version of probabilistic Kleene algebra with angelic nondeterminism and a corresponding class of automata. Our approach implements semantics via distributions over multisets in order to overcome theoretical barriers arising from the lack of a distributive law between the powerset and Giry monads. We produce a full Kleene theorem and a coalgebraic theory, as well as both operational and denotational semantics and equational reasoning principles.