An Introduction to Multi-Valued Model Checking

Nowadays computer systems have become ubiquitous. Most of the resources in the development of such systems, and especially in the fail-safe ones, are allocated into the simulation and verification of their behavior. One such automated method of verification is model checking. Given a mathematical description of the real system and a specification usually in the form of temporal logics, a model checker verifies whether the specification is satisfied on the model of the system. Recently, a multi-valued extension to the classical model checking has been proposed. In this approach both the model of the system and the specification take truth values over lattices with more then just two values. Such an extension enhances the expressive power of temporal logics and allows reasoning under uncertainty. Some of the applications that can take advantage of the multi-valued model checking are abstraction techniques, reasoning about conflicting viewpoints and temporal logic query checking. In this paper, we present three different approaches to the multi-valued model checking problem. The first is a reduction from multi-valued CTL∗ to CTL∗, the second a multi-valued CTL symbolic model checking algorithm and, finally, a reduction technique from multi-valued μ-calculus to the classical one.