The Theory of Traces for Systems with Nondeterminism, Probability, and Termination

This paper studies trace-based equivalences for systems combining nondeterministic and probabilistic choices. We show how trace semantics such processes can be recovered by instantiating a coalgebraic construction known as the generalised powerset construction. characterise compare resulting to definitions of appearing in literature. Most our results are based on exciting interplay between monads their presentations via algebraic theories.