A General Setting for Flexibly Combining and Augmenting Decision Procedures
Journal of Automated Reasoning
Using BDDs with Combinations of Theories
LPAR '02 Proceedings of the 9th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
Using Decision Procedures with a Higher-Order Logic
TPHOLs '01 Proceedings of the 14th International Conference on Theorem Proving in Higher Order Logics
A Generalization of Shostak's Method for Combining Decision Procedures
FroCoS '02 Proceedings of the 4th International Workshop on Frontiers of Combining Systems
A Rewrite Rule Based Framework for Combining Decision Procedures
FroCoS '02 Proceedings of the 4th International Workshop on Frontiers of Combining Systems
RTA '02 Proceedings of the 13th International Conference on Rewriting Techniques and Applications
FME '02 Proceedings of the International Symposium of Formal Methods Europe on Formal Methods - Getting IT Right
ICS: Integrated Canonizer and Solver
CAV '01 Proceedings of the 13th International Conference on Computer Aided Verification
Checking Satisfiability of First-Order Formulas by Incremental Translation to SAT
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
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)
A randomized satisfiability procedure for arithmetic and uninterpreted function symbols
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
Lightweight integration of the Ergo theorem prover inside a proof assistant
Proceedings of the second workshop on Automated formal methods
CC(X): Semantic Combination of Congruence Closure with Solvable Theories
Electronic Notes in Theoretical Computer Science (ENTCS)
New results on rewrite-based satisfiability procedures
ACM Transactions on Computational Logic (TOCL)
Automated reasoning: past story and new trends
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
User control and direction of a more efficient simplifier in ACL2
Proceedings of the Eighth International Workshop on the ACL2 Theorem Prover and its Applications
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)
A randomized satisfiability procedure for arithmetic and uninterpreted function symbols
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
Building extended canonizers by graph-based deduction
ICTAC'07 Proceedings of the 4th international conference on Theoretical aspects of computing
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
Rewriting, inference, and proof
WRLA'10 Proceedings of the 8th international conference on Rewriting logic and its applications
Functional equations in shostak theories
CSR'06 Proceedings of the First international computer science conference on Theory and Applications
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
FroCoS'05 Proceedings of the 5th international conference on Frontiers of Combining Systems
Efficient satisfiability modulo theories via delayed theory combination
CAV'05 Proceedings of the 17th international conference on Computer Aided Verification
An algorithm for deciding BAPA: boolean algebra with presburger arithmetic
CADE' 20 Proceedings of the 20th international conference on Automated Deduction
The algebra of equality proofs
RTA'05 Proceedings of the 16th international conference on Term Rewriting and Applications
Producing and verifying extremely large propositional refutations
Annals of Mathematics and Artificial Intelligence
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Abstract: Decision procedures for equality in a combination of theories are at the core of a number of verification systems. Shostak's decision procedure for equality in the combination of solvable and canonizable theories has been around for nearly two decades. Variations of this decision procedure have been implemented in a number of systems including STP, Ehdm , PVS, STeP, and SVC. The algorithm is quite subtle and a correctness argument for it has remained elusive. Shostak's algorithm and all previously published variants of it yield incomplete decision procedures. We describe a variant of Shostak's algorithm along with proofs of termination, soundness, and completeness.