Towards mechanical metamathematics
Journal of Automated Reasoning
Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
A mechanical proof of the Church-Rosser theorem
Journal of the ACM (JACM)
Formal Verification for Fault-Tolerant Architectures: Prolegomena to the Design of PVS
IEEE Transactions on Software Engineering
GRASP: A Search Algorithm for Propositional Satisfiability
IEEE Transactions on Computers
A Computing Procedure for Quantification Theory
Journal of the ACM (JACM)
Model checking
A machine program for theorem-proving
Communications of the ACM
Chaff: engineering an efficient SAT solver
Proceedings of the 38th annual Design Automation Conference
Principles and Pragmatics of Subtyping in PVS
WADT '99 Selected papers from the 14th International Workshop on Recent Trends in Algebraic Development Techniques
SATO: An Efficient Propositional Prover
CADE-14 Proceedings of the 14th International Conference on Automated Deduction
Trust and Automation in Verification Tools
ATVA '08 Proceedings of the 6th International Symposium on Automated Technology for Verification and Analysis
Formalization and Implementation of Modern SAT Solvers
Journal of Automated Reasoning
A tutorial on satisfiability modulo theories
CAV'07 Proceedings of the 19th international conference on Computer aided verification
versat: a verified modern SAT solver
VMCAI'12 Proceedings of the 13th international conference on Verification, Model Checking, and Abstract Interpretation
Mechanical verification of SAT refutations with extended resolution
ITP'13 Proceedings of the 4th international conference on Interactive Theorem Proving
Formally Verified Tableau-Based Reasoners for a Description Logic
Journal of Automated Reasoning
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Recent years have witnessed dramatic improvements in the capabilities of propositional satisfiability procedures or SAT solvers. The speedups are the result of numerous optimizations including conflict-directed backjumping. We use the Prototype Verification System (PVS) to verify a satisfiability procedure based on the Davis-Putnam-Logemann-Loveland (DPLL) scheme that features these optimizations. This exercise is a step toward the verification of an efficient implementation of the satisfiability procedure. Our verification of a SAT solver is part of a larger program of research to provide a secure foundation for inference using a verified reference kernel that contains a verified SAT solver. Our verification exploits predicate subtypes and dependent types in PVS to capture the specification and the key invariants.