Symbolic Bisimulations for Probabilistic Systems

The paper introduces symbolic bisimulations for a simple probabilistic pi-calculus to overcome the infinite branching problem that still exists in checking ground bisimulations between probabilistic systems. Especially the definition of weak (symbolic) bisimulation does not rely on the random capability of adversaries and suggests a solution to the open problem on the axiomatization for weak bisimulation in the case of unguarded recursion. Furthermore, we present an efficient characterization of symbolic bisimulations for the calculus, which allows the "on-the-fly" instantiation of bound names and dynamic construction of equivalence relations for quantitative evaluation. This directly results in a local decision algorithm that can explore just a minimal portion of the state spaces of the probabilistic processes in question.