Symbolic execution is an intuitive strategy to verify sequential programs, which can be automated to a large extent. We have successfully carried over this method of proof to the interactive verification of concurrent systems. The resulting strategy can be applied to the verification of complex parallel programs and arbitrary (linear) temporal formulas. Our underlying logic is defined such that operators for parallel programs and temporal logic can be arbitrarily nested. We support interleaving with explicit blocking, nondeterministic choice, and others. Most important, the semantics of all of the operators are compositional. Thus, systems can be abstracted and proofs can be decomposed. This ensures that our strategy of proof can be applied to the verification of large, concurrent systems.

HIS BOOK CONTAINS a most comprehensive text that presents syntax-directed and compositional methods for the formal veri?- T cation of programs. The approach is not language-bounded in the sense that it covers a large variety of programming models and features that appear in most modern programming languages. It covers the classes of - quential and parallel, deterministic and non-deterministic, distributed and object-oriented programs. For each of the classes it presents the various c- teria of correctness that are relevant for these classes, such as interference freedom, deadlock freedom, and appropriate notions of liveness for parallel programs. Also, special proof rules appropriate for each class of programs are presented. In spite of this diversity due to the rich program classes cons- ered, there exist a uniform underlying theory of veri?cation which is synt- oriented and promotes compositional approaches to veri?cation, leading to scalability of the methods. The text strikes the proper balance between mathematical rigor and - dactic introduction of increasingly complex rules in an incremental manner, adequately supported by state-of-the-art examples. As a result it can serve as a textbook for a variety of courses on di?erent levels and varying durations. It can also serve as a reference book for researchers in the theory of veri?- tion, in particular since it contains much material that never before appeared in book form. This is specially true for the treatment of object-oriented p- grams which is entirely novel and is strikingly elegant.

gramatKoreaUniversityandtheDepartmentofComputerScienceatKAISTfor ?nancialsupport. We sincerely hope that the readers ?nd the proceedings of ATVA 2008 informative and rewarding.

This book constitutes the refereed proceedings of the Fourth International Symposium on NASA Formal Methods, NFM 2012, held in Norfolk, VA, USA, in April 2012. The 36 revised regular papers presented together with 10 short papers, 3 invited talks were carefully reviewed and selected from 93 submissions. The topics are organized in topical sections on theorem proving, symbolic execution, model-based engineering, real-time and stochastic systems, model checking, abstraction and abstraction refinement, compositional verification techniques, static and dynamic analysis techniques, fault protection, cyber security, specification formalisms, requirements analysis and applications of formal techniques.

Abstract: "The traditional approach to symbolic execution of concurrent programs relies on interleaving the execution of sequential components to model concurrency. This approach suffers from well-known combinatorial problems, making it unsuitable for formal verification. The paper describes an alternate approach that directly supports formal verification. Symbolic execution is based on an axiomatic proof system for concurrent programs, in which processes are verified separately and then checked for cooperation.