Quantitative Computation Tree Logic Model Checking Based on Generalized Possibility Measures

Abstract

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. Based on generalized possibility measures and generalized necessity measures, the method of generalized possibilistic computation tree logic model checking is discussed, and the corresponding algorithm and its complexity are shown in detail. Furthermore, the comparison between PoCTL introduced in [20,25] and GPoCTL is given. Finally, a thermostat example is given to illustrate the GPoCTL model-checking method.

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.…”

“…[22] A generalized possibilistic Kripke structure (GPKS, in short) is a tuple M = (S, P, I, AP, L), where (1) S is a countable, nonempty set of states;(2) P : S × S −→ [0, 1] is a function, called possibilistic transition distribution function; (3) I : S −→ [0, 1] is a function, called possibilistic initial distribution function; AP is a set of atomic propositions; (5) L : S × AP −→ [0, 1] is a possibilistic labeling function, which can be viewed as function mapping a state s to the fuzzy set of atomic propositions which are possible in the state s, i.e., L(s, a) denotes the possibility or truth value of atomic proposition a that is supposed to hold in s. Furthermore, if the set S and AP are finite sets, then M = (S, P, I, AP, L) is called a finite generalized possibilistic Kripke structure. In Definition 1, if we require the transition possibility distribution…”

“…[22] Let M be a finite GPKS. Then the possibility measure of the cylinder sets is given by Po(Cyl(s 0 · · · s n )) = I(s 0 ) ∧n−1 i=0 P(s i , s i+1 ) ∧ r P (s n ) when n > 0 and Po(Cyl(s 0 )) = I(s 0 ) ∧ r P (s 0 ).…”

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

“…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 checking of non-additive systems.…”

“…Li et al proposed Generalized Possibilistic LTL (GPoLTL), which is an extension of LTL, and gave quantitative model checking methods of linear-time properties based on generalized possibility measures in [18]. They also extended CTL to Generalized Possibilistic CTL (GPoCTL) and proposed a model-checking algorithm under the generalized possibilistic decision process in [21]. Our paper is the first to extend classical µ-calculus in possibility measure theory, and it studies the possibilistic model checking.…”