Quantitative Model Checking of Linear-Time Properties Based on Generalized Possibility Measures

TL;DR

This paper develops a quantitative model checking framework for fuzzy linear-time properties using generalized possibility measures, extending previous qualitative approaches to incorporate uncertainty in system models and properties.

Contribution

It introduces generalized possibilistic Kripke structures and studies verification of fuzzy linear-time properties, including safety and liveness, using fuzzy automata.

Findings

Verification reduces to reachability and persistence checks in product structures.

Fuzzy regular safety and ω-regular properties can be verified using fuzzy automata.

The methods are illustrated with concrete examples.

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 {\sl 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 $\omega-$regular properties in GPKSs are introduced, the verification of fuzzy regular safety properties and fuzzy $\omega-$regular properties using fuzzy finite automata are thoroughly studied. It has been shown that the verification of fuzzy regular safety properties and fuzzy $\omega-$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.