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Non-deterministic (also known as possibilistic) and probabilistic state based systems (or automata) have been studied for quite some time. Separately, they are reasonably well-understood. The combination however is difficult, both for conceptual and technical reasons. Here we study the combination from a coalgebraic perspective and identify a monad CM that captures the combination—following work of Varacca. We use this monad to apply the coalgebraic framework for (finite) trace semantics in this setting. It yields a smooth, but not entirely trivial, description of traces

Coalgebraic Trace Semantics for Combined Possibilitistic and Probabilistic Systems