Introduction to algorithms
Equational formulae with membership constraints
Information and Computation
Fast Decision Procedures Based on Congruence Closure
Journal of the ACM (JACM)
Reasoning About Recursively Defined Data Structures
Journal of the ACM (JACM)
Variations on the Common Subexpression Problem
Journal of the ACM (JACM)
A decision procedure for term algebras with queues
ACM Transactions on Computational Logic (TOCL)
Knuth-Bendix Constraint Solving Is NP-Complete
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
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LICS '00 Proceedings of the 15th Annual IEEE Symposium on Logic in Computer Science
Structural Subtyping of Non-Recursive Types is Decidable
LICS '03 Proceedings of the 18th Annual IEEE Symposium on Logic in Computer Science
Presburger arithmetic with bounded quantifier alternation
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
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Decision procedures for term algebras with integer constraints
Information and Computation - Special issue: Combining logical systems
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CADE' 20 Proceedings of the 20th international conference on Automated Deduction
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TACAS'06 Proceedings of the 12th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Modular termination and combinability for superposition modulo counter arithmetic
FroCoS'11 Proceedings of the 8th international conference on Frontiers of combining systems
An efficient and secure approach for a cloud collaborative editing
Journal of Network and Computer Applications
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Balanced search trees provide guaranteed worst-case time performance and hence they form a very important class of data structures. However, the self-balancing ability comes at a price; balanced trees are more complex than their unbalanced counterparts both in terms of data structure themselves and related manipulation operations. In this paper we present a framework to model balanced trees in decidable first-order theories of term algebras with Presburger arithmetic. In this framework, a theory of term algebras (i.e., a theory of finite trees) is extended with Presburger arithmetic and with certain connecting functions that map terms (trees) to integers. Our framework is flexible in the sense that we can obtain a variety of decidable theories by tuning the connecting functions. By adding maximal pathand minimal pathfunctions, we obtain a theory of red-black trees in which the transition relation of tree self-balancing (rotation) operations is expressible. We then show how to reduce the verification problem of the red-black tree algorithm to constraint satisfiability problems in the extended theory.