Probabilistic mediator: A coalgebraic perspective

Mediator is a component-based modeling language where components and systems can be specified separately and precisely. In this paper, we show how to analyze probabilistic Mediator, which supports both non-deterministic and probabilistic behavior of component-based systems, from a coalgebraic perspective. Probabilistic Mediator components are modeled as coalgebras, with the powerset monad P and the distribution monad D to capture their non-determinsitic and probabilistic behavior, respectively. A coalgebraic semantics of combinators on Mediator components is developed. Such a coalgebraic view induces a suitable notion of bisimulation for comparing probabilistic Mediator components and systems.