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This volume contains those research papers presented at the Second International Conference on Tests and Proofs (TAP 2008) that were not included in the main conference proceedings. TAP was the second conference devoted to the convergence of proofs and tests. It combines ideas from both areas for the advancement of software quality. To prove the correctness of a program is to demonstrate, through impeccable mathematical techniques, that it has no bugs; to test a program is to run it with the expectation of discovering bugs. On the surface, the two techniques seem contradictory: if you have proved your program, it is fruitless to comb it for bugs; and if you are testing it, that is surely a sign that you have given up on any hope of proving its correctness. Accordingly, proofs and tests have, since the onset of software engineering research, been pursued by distinct communities using rather different techniques and tools. And yet the development of both approaches leads to the discovery of common issues and to the realization that each may need the other. The emergence of model checking has been one of the first signs that contradiction may yield to complementarity, but in the past few years an increasing number of research efforts have encountered the need for combining proofs and tests, dropping earlier dogmatic views of their incompatibility and taking instead the best of what each of these software engineering domains has to offer. The first TAP conference (held at ETH Zurich in February 2007) was an attempt to provide a forum for the cross-fertilization of ideas and approaches from the testing and proving communities. For the 2008 edition we found the Monash University Prato Centre near Florence to be an ideal place providing a stimulating environment. We wish to sincerely thank all the authors who submitted their work for consideration. And we would like to thank the Program Committee members as well as additional referees for their great effort and professional work in the review and selection process. Their names are listed on the following pages. In addition to the contributed papers, the program included three excellent keynote talks. We are grateful to Michael Hennell (LDRA Ltd., Cheshire, UK), Orna Kupferman (Hebrew University, Israel), and Elaine Weyuker (AT&T Labs Inc., USA) for accepting the invitation to address the conference. Two very interesting tutorials were part of TAP 2008: "Parameterized Unit Testing with Pex" (J. de Halleux, N. Tillmann) and "Integrating Verification and Testing of Object-Oriented Software" (C. Engel, C. Gladisch, V. Klebanov, and P. Rümmer). We would like to express our thanks to the tutorial presenters for their contribution. It was a team effort that made the conference so successful. We are grateful to the Conference Chair and the Steering Committee members for their support. And we particularly thank Christoph Gladisch, Beate Körner, and Philipp Rümmer for their hard work and help in making the conference a success. In addition, we gratefully acknowledge the generous support of Microsoft Research Redmond, who financed an invited speaker.