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Abstract. The accuracy of fuzzy time series prediction method depends on the accuracy of the discourse division and fuzzy relation extraction. Aiming at the main problems in the model, this paper put forward a kind of fuzzy time series prediction method based on spectral clustering using spectral clustering dividing time series discourse and calculate the corresponding fuzzy sets to construct fuzzy time series; At the same time using second-order Markov probability model constructing fuzzy relation in fuzzy time series, and then predict the subsequent numerical. Compared with the traditional fuzzy time series prediction method, this method can improve the accuracy.

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Introduction: Model checking is always considered as a logical analysis of a programme which evolves various challenges in the stages of verification. The abstraction model checking reduces the complexity of the process by translating the programme into a scale down version. Main challenge of model checking is that the space explosion may lead to a verification failure because of limited memory, timeout or space out. This giving-up result was never reported back before, which wouldn't provide analysts much useful information about the system. Aim: The process of abstraction coding has great relevancy in designing biological systems at molecular level. Development of abstraction hierarchies in biological engineering will help us further in categorizing the biological networks. Materials and methods: This paper combines several state-of-art model checkers, and adjusts predicate abstraction blocks dynamically during the verification of biological sequences. In this way when it comes to a verification failure, our algorithm will record and report an abstract version of path from the starting state to the current one. The reported paths could be used as an evidence for designers to review the programs. Results and conclusion: Our experiments show that based on the advantages of implementing different model checkers serially, we use message-passing to execute our algorithm to obtain a better performance. At last the parallel version of our methods outperform some of the popular algorithms as the system scale grows, which has wide applications in computer, biomedical and other disciplines.