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

This paper investigates equivalences within multi-valued systems. We propose a comprehensive set of concepts related to multi-valued equivalences, such as multi-valued simulation equivalence and multi-valued bisimulation equivalence. We conduct an in-depth examination of the associated theorems and lemmas and provide a detailed comparison of these equivalence techniques to highlight their similarities and differences. To address the issue of state space explosion in multi-valued systems, we introduce the concept of multi-valued quotients based on multi-valued equivalences. Additionally, we present a series of related algorithms to implement and apply these multi-valued quotients.