Complete Proof Systems for Amortised Probabilistic Bisimulations

The notion of amortisation has been integrated in quantitative bisimulations to make long-term behavioral comparisons between nondeterministic systems. In this paper, we present sound and complete proof systems for amortised strong probabilistic bisimulation and its observational congruence on a process algebra with probability and nondeterminism, and prove their soundness and completeness. Our results make it possible to reason about long-term (observable) probabilistic behaviors by syntactic manipulations.