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

Abstract

Model checking of linear-time properties based on possibility measures was studied in previous work (Y. Li and L. Li, Model checking of linear-time properties based on possibility measure, IEEE Transactions on Fuzzy Systems, 21(5)(2013), 842-854). However, the linear-time properties considered in the previous work was classical and qualitative, possibility information of the systems was not considered at all. We shall study quantitative model checking of fuzzy linear-time properties based on generalized possibility measures in the paper. Both the model of the system, as well as the properties the system needs to adhere to, are described using possibility information to identify the uncertainty in the model/properties. The systems are modeled by generalized possibilistic Kripke structures (GPKS, in short), and the properties are described by fuzzy linear-time properties. Concretely, fuzzy linear-time properties about reachability, always reachability, constrain reachability, repeated reachability and persitence in GPKSs are introduced and studied. Fuzzy regular safety properties and fuzzy ω−regular properties in GPKSs are introduced, the verification of fuzzy regular safety properties and fuzzy ω−regular properties using fuzzy finite automata are thoroughly studied. It has been shown that the verification of fuzzy regular safety properties and fuzzy ω−regular properties in a finite GPKS can be transformed into the verification of (always) reachability properties and repeated reachability (persistence) properties in the product GPKS introduced in this paper. Several examples are given to illustrate the methods presented in the paper.

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

“…then r(s) denotes the maximum possibility measure of a path starting from state s. Furthermore, any finite Generalized Possibilistic Kripke Structure (GPKS) [18] can be regarded as a finite GPDP with only one action available in any state.…”

“…We use the intelligent washing machine studied in [18] as an example to better explain the application of the GPo µ model-checking method. As shown in Figure 3, it is the control system of the intelligent washing machine, where S 0 to S 10 are the states of the system, there is only one action in the system, and the possibility values are marked between states.…”

“…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.…”

“…Possibilistic model checking uses the theory of possibility measure as the theoretical basis for system modeling, which is suitable for systems with uncertain information in possibility theory [7].There is some research on quantitative model-checking verification methods on the basis of possibility measures. 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].…”

Fuzzy alternating Büchi automata over distributive lattices

“…The aim of this section is to discuss decision problems for L-fuzzy alternating Büchi automata over a distributive lattice with a negation c. These discussions can be applied to the satisfiability and model-checking problem of fuzzy LTL [15,16].…”