WING 2010: Editor's Preface

Welcome to the first volume of EPiC, the EasyChair Proceedings in Computing. The volume is dedicated to the second and third International Workshop on Invariant Generation (WING 2009 and 2010) workshops. WING 2009 was held on March 29, 2009 in York, UK, as a satellite workshop of the twelfth European Joint Conferences on Theory and Practice of Software (ETAPS 2009), and WING 2010 was held on July 21, 2010 in Edinburgh, as a satellite event of the fifth International Federated Logic Conference (FLoC 2010).

\subsection*{Invariants are forever}

The ability to extract and synthesize auxiliary properties of programs has had a profound effect on program analysis, testing and verification over the last several decades. The field of invariant generation draws on a multitude of techniques ranging from computer algebra, theorem proving, constraint solving, abstract interpretation techniques and model-checking. Likewise are the application areas diversified from bootstrapping static program analysis tools to test-case generation and into aiding the quest for verified software. So invariants are a key ingredient in program analysis and understanding. Yet, invariant generation poses as many challenges as promises: A key impediment for program verification is the overhead associated with providing, debugging, and verifying auxiliary invariant annotations. As the design and implementation of reliable software remains an important issue, any progress in this area will be of utmost importance for future developments in verified software. In the context of static analysis and test-case generation, suitable invariants have the potential of enabling sophisticated automatic program analysis and high-coverage test-case generation.

The field of invariant generation thus benefits an array of applications for program understanding. It draws on many concepts and techniques developed in the context of symbolic computations; including program logics, theorem proving, numerical analysis computer aided verification and deduction, to mention a few.

\subsection*{The WING series}

The WING workshop series aims to bring together researchers from several fields of abstract interpretation, computational logic and computer algebra to support reasoning about loops, in particular, by using algorithmic combinatorics, narrowing/widening techniques, static analysis, polynomial algebra, quantifier elimination and model checking.

The workshops offer an interactive forum for presenting work in progress, new results and follow on experience with established methods.

The first WING 2007 was held as a satellite event of the RISC Summer Conference Series, Hagenberg, Austria -- \url{http://www.risc.uni-linz.ac.at/about/conferences/WING2007/}.

The second edition of the WING workshop was WING 2009, and it was held at ETAPS 2009, York, UK -- see \url{http://mtc.epfl.ch/events/WING09/}. The program of WING 2009 included 7 regular presentations and two invited talks. The invited speakers of WING 2009 were Leonardo de Moura (Microsoft Research, USA) and Andrey Rybalchenko (now at the Technische Universit\"at M\"unchen, Germany)

WING 2010 was the third time the workshop was held. It featured 10 regular presentations and two invited talks. One invited lecture was given by Sumit Gulwani (Microsoft Research, USA), and one by Helmut Seidl (Technische Universit\"at M\"unchen, Germany) on the topic of the first paper published in this special issue. WING 2010 received sponsorship from Microsoft Research. More details about WING 2010 can be found at \url{http://research.microsoft.com/en-us/events/wing2010}.

\subsection*{The WING 2009 and WING 2010 proceedings} This joint proceedings of WING 2009 and WING 2010 contains two invited papers and 17 regular papers. The invited papers of the proceedings are based on the invited talks of Leonardo de Moura and Helmut Seidl from WING 2009 and WING 2010, respectively. The regular papers of this proceedings describe contributions in the area of invariant generation that have been presented at WING 2009 and WING 2010.

We would like to thank the WING 2009 and WING 2010 program committee members and reviewers for all their efforts. We would also like to thank Andrew Ireland (Heriot-Watt University, UK) for co-chairing WING 2009. Thanks also go to the steering committee members of WING for their valuable advice and guidance. Finally, we would like to thank Microsoft Research for their sponsorship at WING 2010.