What is Counterexample

Applying swarm intelligence techniques to software engineering problems has appealed to both researchers and practitioners in the software engineering community. This chapter describes issues and challenges of its application to formal verification, which is one of the core research fields in software engineering. Formal verification, which explores how to effectively verify software products by using mathematical technique, often suffers from two open problems. One is the so-called state explosion problem that verification tools need too many computational resources to make verification feasible. The other problem is that the results of verification have often too much complexity for users to understand. While a number of research projects have addressed these problems in the context of traditional formal verification, recent researches demonstrate that Swarm Intelligence is a promising tool to tackle the problems. This chapter presents how Swarm Intelligence can be applied to formal verification, and surveys the state-of-the-art techniques.