  Labeled state-to-function transition systems, FuTS for short, admit multiple
transition schemes from states to functions of finite support over general
semirings. As such they constitute a convenient modeling instrument to deal
with stochastic process languages. In this paper, the notion of bisimulation
induced by a FuTS is proposed and a correspondence result is proven stating
that FuTS-bisimulation coincides with the behavioral equivalence of the
associated functor. As generic examples, the concrete existing equivalences for
the core of the process algebras ACP, PEPA and IMC are related to the
bisimulation of specific FuTS, providing via the correspondence result
coalgebraic justification of the equivalences of these calculi.
