This book contains the proceedings of VMCAI 2007. It features current research from the communities of verification, program certification, model checking, debugging techniques, abstract interpretation, abstract domains, and advancement of hybrid methods.

Abstract Interpretation of Non-monotone Bi-inductive Semantic Definitions.- CTL as an Intermediate Language.- Multi-valued Logics, Automata, Simulations, and Games.- Verification of Register Allocators.- Program Analysis and Programming Languages for Security.- An Improved Tight Closure Algorithm for Integer Octagonal Constraints.- Handling Parameterized Systems with Non-atomic Global Conditions.- Abstract Interpretation of the Physical Inputs of Embedded Programs.- Diagnostic Information for Realizability.- Approximation Refinement for Interpolation-Based Model Checking.- Abstract Interpretation of Cellular Signalling Networks.- Is Lazy Abstraction a Decision Procedure for Broadcast Protocols?.- Model Checking for Action Abstraction.- On Bridging Simulation and Formal Verification.- Extending Model Checking with Dynamic Analysis.- Deriving Bisimulations by Simplifying Partitions.- Precise Set Sharing Analysis for Java-Style Programs.- Sufficient Preconditions for Modular Assertion Checking.- Runtime Checking for Separation Logic.- Decision Procedures for Multisets with Cardinality Constraints.- All You Need Is Compassion.- A Forward-Backward Abstraction Refinement Algorithm.- Internal and External Logics of Abstract Interpretations.- From LTL to Symbolically Represented Deterministic Automata.- Monitoring Temporal Properties of Stochastic Systems.- A Hybrid Algorithm for LTL Games.

th This volumecontains the proceedingsof the 9 internationalconference onV- i?cation, Model Checking, and Abstract Interpretation (VMCAI 2008), held in San Francisco, January 7 9, 2008. The purpose of VMCAI is to provide a forum for researchers from three communities Veri?cation, Model Checking, and - stractInterpretation thatwill facilitate interaction,cross-fertilization,andthe advance of hybridmethods that combine the three areas.With the growingneed for formal tools to reason about complex, in?nite-state, and embedded systems, such hybrid methods are bound to be of great importance. Topics covered by VMCAI include program veri?cation, program certi?- tion, model checking, debugging techniques, abstract interpretation, abstract domains, static analysis, type systems, deductive methods, and optimization. VMCAI 2008 was the 9th VMCAI meeting. Previous meetings were held in Port Je?erson 1997, Pisa 1998, Venice 2002, New York 2003, Venice 2004, Paris 2005, Charleston 2006, and Nice 2007. The program committee selected 21 papers out of over 60 on the basis of at least three reviews. The principal criteria were relevance and quality. The program of VMCAI 2008 included, in addition to the research papers, three invited talks, by Radhia Cousot, Maurice Herlihy and Neil Jones, and three tutorials, by Orna Kupferman, Jens Palsberg, and Marco Pistoia. We would like to thank the ProgramCommittee members and the reviewers, without whose dedicated e?ort the conference would not have been possible. Our thanks also to the Steering Committee members for their helpful advice.