Incremental model checking for fuzzy computation tree logic

Fuzzy model checking, also called multi-valued model checking, has proved to be an effective technique in verifying properties of fuzzy systems. One important issue with fuzzy model checking, is that a model adopted in fuzzy model checking is frequently updated with small changes, and it is too costly to run a model-checking algorithm from scratch in response to every update. To address the issue, in this paper, we consider the incremental model-checking approach for fuzzy systems by making maximal use of previous model checking results or in other words, by minimizing unnecessary recomputation. The models of our study are fuzzy Kripke structures, which are a fuzzy counterpart of Kripke structures and used to describe fuzzy systems, while the properties of fuzzy systems are expressed using fuzzy computation tree logic, a fuzzy temporal logic derived from computation tree logic. The focus of the paper is on how to design incremental model-checking algorithms for two until-formulas which characterize the maximal or dually minimum constrained reachability properties with respect to fuzzy Kripke structures under transition insertions or deletions but not both. The feasibility of our approach is illustrated by an example arising from the path planning problem of mobile robots.