A Simple Characterization of Stuttering Bisimulation

Abs t r ac t . Showing equivalence of two systems at different levels of abstraction often entails mapping a single step in one system to a sequence of steps in the other, where the relevant state information does not change until the last step. In [BCG 88,dNV 90], bisimulations that take into account such "stuttering" are formulated. These definitions are, however, difficult to use in proofs of bisimulation, as they often require one to exhibit a finite, but unbounded sequence of transitions to match a single transition; thus introducing a large number of proof obligations. We present an alternative formulation of bisimulation under stuttering, in terms of a ranking function over a well-founded set. It has the desirable property, shared with strong bisimulation [Mil 90], that it requires matching 8ingle transitions only, which considerably reduces the number of proof obligations. This makes proofs of bisimulation short, and easier to demonstrate and understand. We show that the new formulation is equivalent to the original one, and illustrate its use with non-trivial examples that have infinite state spaces and exhibit unbounded stuttering.