A practical algorithm for exact array dependence analysis
Communications of the ACM
On Fourier's algorithm for linear arithmetic constraints
Journal of Automated Reasoning
Fast Decision Procedures Based on Congruence Closure
Journal of the ACM (JACM)
Variations on the Common Subexpression Problem
Journal of the ACM (JACM)
Deciding Combinations of Theories
Journal of the ACM (JACM)
Simplification by Cooperating Decision Procedures
ACM Transactions on Programming Languages and Systems (TOPLAS)
An algorithm for reasoning about equality
Communications of the ACM
Reasoning about recursively defined data structures
POPL '78 Proceedings of the 5th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Validity Checking for Combinations of Theories with Equality
FMCAD '96 Proceedings of the First International Conference on Formal Methods in Computer-Aided Design
Rewriting, Decision Procedures and Lemma Speculation for Automated Hardware Verification
TPHOLs '97 Proceedings of the 10th International Conference on Theorem Proving in Higher Order Logics
A Rewrite Rule Based Framework for Combining Decision Procedures
FroCoS '02 Proceedings of the 4th International Workshop on Frontiers of Combining Systems
Shostak's Congruence Closure as Completion
RTA '97 Proceedings of the 8th International Conference on Rewriting Techniques and Applications
Uniform Derivation of Decision Procedures by Superposition
CSL '01 Proceedings of the 15th International Workshop on Computer Science Logic
A Mechanizable Induction Principle for Equational Specifications
Proceedings of the 9th International Conference on 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
Extending Decision Procedures with Induction Schemes
CADE-17 Proceedings of the 17th International Conference on Automated Deduction
Decidable Classes of Inductive Theorems
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
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
A Rewrite Rule Based Framework for Combining Decision Procedures
FroCoS '02 Proceedings of the 4th International Workshop on Frontiers of Combining Systems
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)
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)
Strategies for combining decision procedures
TACAS'03 Proceedings of the 9th international conference on Tools and algorithms for the construction and analysis of systems
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
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A rewrite rule based framework for combining decision procedures for universally quantified theories is proposed. It builds on the key ideas of Shostak's combination approach. A distinctive feature of the proposed framework is that its soundness and completeness can be easily established. Furthermore, the framework has the desired property of being efficient (by avoiding duplication of equality reasoning in all decision procedures) as well as generating canonical forms as in Shostak's combination framework. It thus enables tight integration of decision procedures with equational and inductive reasoning based on rewriting.