Possibilistic Cost Computation Tree Logic and Related Equivalence, Abstraction Technique

Abstract

Recently, probabilistic Kripke structures have been used to represent uncertain systems; nevertheless, important transition costs were ignored in earlier studies, making it impossible to model some uncertain systems with costs. To compensate for the major shortcoming, this research addresses the transition costs suggested in uncertain systems. First of all, we offer possibilistic Kripke cost structures and associated possibilistic costs such as cumulative cost and possibilistic expected cost. As the verification model, furthermore, we investigated the syntax and semantics of possibilistic cost computation tree logic and utilized them to develop verification characteristics of possibilistic Kripke cost structures. Finally, as solutions to the state space explosion problem of possibilistic cost computation tree logic model checking, abstraction and equivalence are presented as methods to reduce the state numbers and frameworks of possibilistic Kripke cost structures.

Exploring Equivalences in Multi-Valued Systems: Concepts, Properties, and Generation Methods

“…Focused on the transition relation, Haiyu Pan introduced lattice-valued bisimulation as an equivalence of lattice-valued transition systems [22]. Integrating the cost problem within possibilistic Kripke structures, Deng introduced the concept of possibilistic cost bisimulation as an equivalence [23].…”