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Journal of Logic Programming
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A Computing Procedure for Quantification Theory
Journal of the ACM (JACM)
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Journal of the ACM (JACM)
Handbook of logic in computer science
POPL '77 Proceedings of the 4th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Systematic design of program analysis frameworks
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From Pre-Historic to Post-Modern Symbolic Model Checking
Formal Methods in System Design
Combining abstract interpreters
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Logical Interpretation: Static Program Analysis Using Theorem Proving
CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
Generalizing DPLL to Richer Logics
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Natural domain SMT: a preliminary assessment
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HVC'09 Proceedings of the 5th international Haifa verification conference on Hardware and software: verification and testing
Efficient CNF simplification based on binary implication graphs
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Using bounded model checking to focus fixpoint iterations
SAS'11 Proceedings of the 18th international conference on Static analysis
Effective preprocessing in SAT through variable and clause elimination
SAT'05 Proceedings of the 8th international conference on Theory and Applications of Satisfiability Testing
Yet another decision procedure for equality logic
CAV'05 Proceedings of the 17th international conference on Computer Aided Verification
Numeric bounds analysis with conflict-driven learning
TACAS'12 Proceedings of the 18th international conference on Tools and Algorithms for the Construction and Analysis of Systems
A method for symbolic computation of abstract operations
CAV'12 Proceedings of the 24th international conference on Computer Aided Verification
Theories, solvers and static analysis by abstract interpretation
Journal of the ACM (JACM)
Satisfiability solvers are static analysers
SAS'12 Proceedings of the 19th international conference on Static Analysis
A generalization of stålmarck's method
SAS'12 Proceedings of the 19th international conference on Static Analysis
Abstract conflict driven learning
POPL '13 Proceedings of the 40th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
SAT'13 Proceedings of the 16th international conference on Theory and Applications of Satisfiability Testing
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This article introduces an abstract interpretation framework that codifies the operations in SAT and SMT solvers in terms of lattices, transformers and fixed points. We develop the idea that a formula denotes a set of models in a universe of structures. This set of models has characterizations as fixed points of deduction, abduction and quantification transformers. A wide range of satisfiability procedures can be understood as computing and refining approximations of such fixed points. These include procedures in the DPLL family, those for preprocessing and inprocessing in SAT solvers, decision procedures for equality logics, weak arithmetics, and procedures for approximate quantification. Our framework provides a unified, mathematical basis for studying and combining program analysis and satisfiability procedures. A practical benefit of our work is a new, logic-agnostic architecture for implementing solvers.