Computation tree logic model checking based on possibility measures

Abstract

In order to deal with the systematic verification with uncertain infromation in possibility theory, Li and Li [19] introduced model checking of linear-time properties in which the uncertainty is modeled by possibility measures. Xue, Lei and Li [26] defined computation tree logic (CTL) based on possibility measures, which is called possibilistic CTL (PoCTL). This paper is a continuation of the above work. First, we study the expressiveness of PoCTL. Unlike probabilistic CTL, it is shown that PoCTL (in particular, qualitative PoCTL) is more powerful than CTL with respect to their expressiveness. The equivalent expressions of basic CTL formulae using qualitative PoCTL formulae are presented in detail. Some PoCTL formulae that can not be expressed by any CTL formulae are presented. In particular, some qualitative properties of repeated reachability and persistence are expressed using PoCTL formulae. Next, adapting CTL model-checking algorithm, a method to solve the PoCTL model-checking problem and its time complexity are discussed in detail. Finally, an example is given to illustrate the PoCTL model-checking method.

Quantitative Computation Tree Logic Model Checking Based on Generalized Possibility Measures

“…In this section, we give some basic knowledge about the possibility theory, and recall the possibilistic computation tree logic (PoCTL, in short) introduced in [20].…”

“…We can see that even in a PKS as in Fig.3, the path formula a in GPoCTL is not crisp. As we know, all formulae in PoCTL, including state and path formulae, are crisp, see [20]. The semantics of GPoCTL, compared with that of PoCTL, contains more possibility information.…”

“…Furthermore, for the application to quantitative models and quantitative specifications, quantitative model-checking approaches have been proposed recently. Different approaches are applicable to different models types including timed ( [1]), probabilistic and stochastic ( [15]), multi-valued ( [2][3][4]), quality of service or soft constraints ( [21]), discounted sources-restricted ( [5]), possibilistic ( [20]), etc, methods.…”

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We study generalized possibilistic computation tree logic model checking in this paper, which is an extension of possibilistic computation logic model checking introduced by Y.Li, Y.Li and Z.Ma [20]. The system is modeled by generalized possibilistic Kripke structures (GPKS, in short), and the verifying property is specified by a generalized possibilistic computation tree logic (GPoCTL, in short) formula.

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Quantitative model checking of linear-time properties based on generalized possibility measures

“…Furthermore, for the application to quantitative models and quantitative specifications, quantitative model-checking approaches have been proposed recently. Different approaches are applicable to different models types including timed ( [2]), probabilistic and stochastic ( [14]), multi-valued ( [3][4][5]), quality of service or soft constraints ( [24]), discounted sources-restricted ( [1,6]), possibilistic ( [20][21][22]) or fuzzy ( [12,25,26], etc, methods.…”