The μ-Calculus Model-Checking Algorithm for Generalized Possibilistic Decision Process

Abstract

Model checking is a formal automatic verification technology for complex concurrent systems. It is used widely in the verification and analysis of computer software and hardware systems, communication protocols, security protocols, etc. The generalized possibilistic µ-calculus model-checking algorithm for decision processes is studied to solve the formal verification problem of concurrent systems with nondeterministic information and incomplete information on the basis of possibility theory. Firstly, the generalized possibilistic decision process is introduced as the system model. Then, the classical proposition µ-calculus is improved and extended, and the concept of generalized possibilistic µ-calculus (GPo µ ) is given to describe the attribute characteristics of nondeterministic systems. Then, the GPo µ model-checking algorithm is proposed, and the model-checking problem is simplified to fuzzy matrix operations. Finally, a specific example and a case study are analyzed and verified. Compared with the classical µ-calculus, the generalized possibilistic µ-calculus has a stronger expressive power and can better characterize the attributes of nondeterministic systems. The model-checking algorithm can give the possibility that the system satisfies the attributes. The research work provides a new idea and method for model checking nondeterministic systems.Appl. Sci. 2020, 10, 2594 2 of 15 have proposed quantitative extensions to classical model checking, such as models that embed features into probability [5,6], possibility [7][8][9], and multi-valued [10][11][12], etc.Different model-checking approaches are applicable to different model types. Narasimha et al.[13] proposed a model-checking algorithm based on the probabilistic labeled transition systems and µ-calculus to check whether the states in the finite probabilistic labeled transition systems satisfiy the logical formulas; Chechik et al. [14] extended the classical CTL and Kripke structure and proposed a multi-valued model checking algorithm. Gurfinkel et al. [15] studied the multi-valued µ-calculus model checking problem based on multi-valued Kripke structures and reduced it into several classical model-checking problems. The advantage of the reduction method is that the verification can be done automatically using existing model-checking tools. Mallya et al. [16] defined a multi-valued µ-calculus and proposed a new model-checking logic framework to verify arbitrary properties of multi-valued µ-calculus, which is more widely used.Recently, Pan et al. [17] combined fuzzy logic with CTL, proposed Fuzzy Computation Tree Logic (FCTL), which is a fuzzy extension of classical CTL, and discussed model-checking problems. Li et al. [18][19][20][21] extended the classical LTL and CTL model-checking technology; they defined a quantitative model-checking verification method on the basis of possibility measures. Compared to probabilistic model checking, the possibilistic model checking does not need to satisfy countable additivity, and it is mainly used for the model ch...