This book constitutes the thoroughly refereed post-proceedings of the First Combined International Workshops on Formal Approaches to Software Testing, FATES 2006, and on Runtime Verification, RV 2006, held within the scope of FLoC 2006, the Federated Logic Conference in Seattle, WA, USA in August 2006.

The 14 revised full papers presented together with 3 invited lectures were carefully selected from 31 initial submissions. The papers discuss formal approaches to test and analyze programs and monitor and guide their executions by using techniques from areas like theorem proving, model checking, constraint resolution, static program analysis, abstract interpretation, Markov chains, and various others. Formal approaches to runtime verification use formal techniques to improve traditional ad-hoc monitoring techniques used in testing, debugging, performance monitoring, fault protection, etc.

This volume constitutes the proceedings of the16th International Conference on Theorem Proving in Higher Order Logics (TPHOLs 2003) held September 8 12, 2003 in Rome, Italy. TPHOLs covers all aspects of theorem proving in higher order logics as well as related topics in theorem proving and veri?cation. TPHOLs 2003 was co-located with TABLEAUX, the International Con- rence on Automated Reasoning with Analytic Tableaux and Related Methods, and with Calculemus, the Symposium on the Integration of Symbolic Compu- tion and Mechanized Reasoning. There were 50 papers submitted to TPHOLs in the full research category, each of which was refereed by at least 3 reviewers, selected by the program c- mittee.Ofthesesubmissions,21wereacceptedforpresentationattheconference and publication in this volume. In keeping with tradition, TPHOLs 2003 also o?ered a venue for the presentation of work in progress, where researchers - vite discussion by means of a brief preliminary talk and then discuss their work at a poster session. A supplementary proceedings containing associated papers for work in progress was published by the computer science department at the Universit] at Freiburg. The organizers are grateful to Jean-Raymond Abrial, Patrick Lincoln, and Dale Miller for agreeing to give invited talks at TPHOLs 2003. The TPHOLs conference traditionally changes continent each year in order to maximize the chances that researchers from around the world can attend."

This book constitutes the refereed proceedings of the 12th International Conference on Tests and Proofs, TAP 2018, held as part of STAF 2018, in Toulouse, France, in June 2018. The 8 regular papers, 2 short papers, 1 invited paper and 1 invited tutorial presented in this volume were carefully reviewed and selected from 18 submissions. The TAP conference promotes research in verification and formal methods that targets the interplay of proofs and testing: the advancement of techniques of each kind and their combination, with the ultimate goal of improving software and system dependability.