Recently, by defining suitable fuzzy temporal logics, temporal properties of dynamic systems are specified during model checking process, yet a few numbers of fuzzy temporal logics along with capable corresponding models are developed and used in system design phase, moreover in case of having a suitable model, it suffers from the lack of a capable model checking approach. Having to deal with uncertainty in model checking paradigm, this paper introduces a fuzzy Kripke model (FzKripke) and then provides a verification approach using a novel logic called Fuzzy Computation Tree Logic* (FzCTL*). Not only state space explosion is handled using well-known concepts like abstraction and bisimulation, but an approximation method is also devised as a novel technique to deal with this problem. Fuzzy program graph, a generalization of program graph and FzKripke, is also introduced in this paper in consideration of higher level abstraction in model construction. Eventually modeling, and verification of a multi-valued flip-flop is studied in order to demonstrate capabilities of the proposed models.

Few fuzzy temporal logics and modeling formalisms are developed such that their model checking is both effective and efficient. State-space explosion makes model checking of fuzzy temporal logics inefficient. That is because either the modeling formalism itself is not compact, or the verification approach requires an exponentially larger yet intermediate representation of the modeling formalism. To exemplify, Fuzzy Program Graph (FzPG) is a very compact, and powerful formalism to model fuzzy systems; yet, it is required to be translated into an equal Fuzzy Kripke model with an exponential blow-up should it be formally verified. In this paper, we introduce Fuzzy Computation Tree Logic (FzCTL) and its direct symbolic model checking over FzPG that avoids the aforementioned state-space explosion. Considering compactness and readability of FzPG along with expressiveness of FzCTL, we believe the proposed method is applicable in real-world scenarios. Finally, we study formal verification of fuzzy flip-flops to demonstrate capabilities of the proposed method.

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