Distribution-Based Behavioral Distance for Nondeterministic Fuzzy Transition Systems
Hengyang Wu, Yuxin Deng · IEEE Transactions on Fuzzy Systems · 2017
Modal logics and behavioral equivalences play an important role in the specification and verification of concurrent systems. In this paper, we first present a new notion of bisimulation for nondeterministic fuzzy transition systems, which is distribution based and coarser than state-based bisimulation appeared in the literature. Then, we define a distribution-based bisimilarity metric as the least fixed point of a suitable monotonic function on a complete lattice, which is a behavioral distance and is a more robust way of formalizing behavioral similarity between states than bisimulations. We also propose an on-the-fly algorithm for computing the bisimilarity metric. Moreover, we present a fuzzy modal logic and provide a sound and complete characterization of the bisimilarity metric. Interestingly, this characterization holds for a class of fuzzy modal logics. In addition, we show the nonexpansiveness of a typical parallel composition operator with respect to the bisimilarity metric, which makes compositional verification possible.