Introduction

The cause of the catastrophic crash of the Ariane 5 rocket in 1996 was traced to a simple problem in the computer software that calculated the rocket’s position. Despite rigorous testing of the software, the problem went unnoticed. Such software failures occur every day – though usually with less spectacular consequences.

How can one insure that computer programs actually do what they are intended to do? Simply running a program repeatedly with various inputs is inadequate, because one cannot tell which inputs might cause the program to fail. It is possible to tailor a tester to test a given program, but present-day programs are so complex that they cannot be adequately checked through conventional testing, which can leave significant bugs undetected. Program verification uses mathematical and logical methods to prove that a program is correct. This approach was pioneered by, among others, Dijkstra, Floyd, Gries, Hoare, Lamport, Manna, Owicki and Pnueli. In the early years of verification research, the focus was on deductive proof systems. Back then, program verification was mostly done manually. Today, we have powerful decision procedures that can, completely automatically, answer basic questions about the data types typically used by programmers. Model Checking is a “push-button” technology that can analyze finite-state abstractions of programs with as many as 10^20^ states. Verification research continues actively in both academia and industry (see conferences like CAV and TACAS, and verification projects by IBM, Microsoft, Bell Labs and many others).

This course takes an up-to-date look at the theory and practice of program verification.