Modularization and abstraction: The keys to practical formal verification

In spite of the impressive progress in the development of the two main methods for formal verification of reactive systems - Model Checking (in particular symbolic) and Deductive Verification, they are still limited in their ability to handle large systems. It is generally recognized that the only way these methods can ever scale up is by the extensive use of abstraction and modularization, which breaks the task of verifying a large system into several smaller tasks of verifying simpler systems. In this methodological paper, we review the two main tools of compositionality and abstraction in the framework of linear temporal logic. We illustrate the application of these two methods for the reduction of an infinite-state system into a finite-state system that can then be verified using model checking. The modest technical contributions contained in this paper are a full formulation of abstraction when applied to a system with both weak and strong fairness requirements and to a general temporal formula, and a presentation of a compositional framework for shared variables and its application for forming network invariants.