Deciding Combinations of Theories
Journal of the ACM (JACM)
Simplification by Cooperating Decision Procedures
ACM Transactions on Programming Languages and Systems (TOPLAS)
Validity Checking for Combinations of Theories with Equality
FMCAD '96 Proceedings of the First International Conference on Formal Methods in Computer-Aided Design
STeP: Deductive-Algorithmic Verification of Reactive and Real-Time Systems
CAV '96 Proceedings of the 8th International Conference on Computer Aided Verification
PVS: A Prototype Verification System
CADE-11 Proceedings of the 11th International Conference on Automated Deduction: Automated Deduction
On Shostak's Decision Procedure for Combinations of Theories
CADE-13 Proceedings of the 13th International Conference on Automated Deduction: Automated Deduction
A Framework for Cooperating Decision Procedures
CADE-17 Proceedings of the 17th International Conference on Automated Deduction
LICS '01 Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science
Integrating decision procedures for temporal verification
Integrating decision procedures for temporal verification
Decision procedures in automated deduction
Decision procedures in automated deduction
Automating Type Soundness Proofs via Decision Procedures and Guided Reductions
LPAR '02 Proceedings of the 9th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
Using BDDs with Combinations of Theories
LPAR '02 Proceedings of the 9th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
RTA '02 Proceedings of the 13th International Conference on Rewriting Techniques and Applications
Simplify: a theorem prover for program checking
Journal of the ACM (JACM)
Canonization for disjoint unions of theories
Information and Computation - Special issue: 19th international conference on automated deduction (CADE-19)
Strategies for combining decision procedures
Theoretical Computer Science - Tools and algorithms for the construction and analysis of systems (TACAS 2003)
Efficient theory combination via boolean search
Information and Computation - Special issue: Combining logical systems
Solving Quantified Verification Conditions Using Satisfiability Modulo Theories
CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
New results on rewrite-based satisfiability procedures
ACM Transactions on Computational Logic (TOCL)
Annals of Mathematics and Artificial Intelligence
Solving quantified verification conditions using satisfiability modulo theories
Annals of Mathematics and Artificial Intelligence
Combination of convex theories: Modularity, deduction completeness, and explanation
Journal of Symbolic Computation
Canonization for disjoint unions of theories
Information and Computation - Special issue: 19th international conference on automated deduction (CADE-19)
An online proof-producing decision procedure for mixed-integer linear arithmetic
TACAS'03 Proceedings of the 9th international conference on Tools and algorithms for the construction and analysis of systems
Strategies for combining decision procedures
TACAS'03 Proceedings of the 9th international conference on Tools and algorithms for the construction and analysis of systems
Combining equational reasoning
FroCoS'09 Proceedings of the 7th international conference on Frontiers of combining systems
On theorem proving for program checking: historical perspective and recent developments
Proceedings of the 12th international ACM SIGPLAN symposium on Principles and practice of declarative programming
Efficient generation of craig interpolants in satisfiability modulo theories
ACM Transactions on Computational Logic (TOCL)
Nelson-Oppen, shostak and the extended canonizer: a family picture with a newborn
ICTAC'04 Proceedings of the First international conference on Theoretical Aspects of Computing
Combining decision procedures by (model-)equality propagation
Science of Computer Programming
FroCoS'05 Proceedings of the 5th international conference on Frontiers of Combining Systems
Building efficient decision procedures on top of SAT solvers
SFM'06 Proceedings of the 6th international conference on Formal Methods for the Design of Computer, Communication, and Software Systems
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Consider the problem of determining whether a quantifier-free formula 酶 is satisfiable in some first-order theory 驴. Shostak's algorithm decides this problem for a certain class of theories with both interpreted and uninterpreted function symbols. We present two new algorithms based on Shostak's method. The first is a simple subset of Shostak's algorithm for the same class of theories but without uninterpreted function symbols. This simplified algorithm is easy to understand and prove correct, providing insight into how and why Shostak's algorithm works. The simplified algorithm is then used as the foundation for a generalization of Shostak's method based on a variation of the Nelson-Oppen method for combining theories.