Decidability of the purely existential fragment of the theory of term algebras
Journal of the ACM (JACM)
Equational problems anddisunification
Journal of Symbolic Computation
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)
Verifying Temporal Properties of Reactive Systems: A STeP Tutorial
Formal Methods in System Design
Simplification by Cooperating Decision Procedures
ACM Transactions on Programming Languages and Systems (TOPLAS)
A decision procedure for term algebras with queues
ACM Transactions on Computational Logic (TOCL)
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
Unions of non-disjoint theories and combinations of satisfiability procedures
Theoretical Computer Science
FroCoS '02 Proceedings of the 4th International Workshop on Frontiers of Combining Systems
Combining Multisets with Integers
CADE-18 Proceedings of the 18th International Conference on Automated Deduction
A Decision Procedure for the Existential Theory of Term Algebras with the Knuth-Bendix Ordering
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
Elementary bounds for presburger arithmetic
STOC '73 Proceedings of the fifth annual ACM symposium on Theory of computing
Presburger arithmetic with bounded quantifier alternation
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Integrating decision procedures for temporal verification
Integrating decision procedures for temporal verification
Model-Theoretic Methods in Combined Constraint Satisfiability
Journal of Automated Reasoning
Arithmetic integration of decision procedures
Arithmetic integration of decision procedures
Decision procedures for queues with integer constraints
FSTTCS '05 Proceedings of the 25th international conference on Foundations of Software Technology and Theoretical Computer Science
The decidability of the first-order theory of knuth-bendix order
CADE' 20 Proceedings of the 20th international conference on Automated Deduction
An algorithm for deciding BAPA: boolean algebra with presburger arithmetic
CADE' 20 Proceedings of the 20th international conference on Automated Deduction
LFCS '07 Proceedings of the international symposium on Logical Foundations of Computer Science
Locality Results for Certain Extensions of Theories with Bridging Functions
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
Decision procedures for algebraic data types with abstractions
Proceedings of the 37th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Quantitative Separation Logic and Programs with Lists
Journal of Automated Reasoning
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Term algebras can model recursive data structures which are widely used in programming languages. To verify programs we must be able to reason about these structures. However, as programming languages often involve multiple data domains, in program verification decision procedures for a single theory are usually not applicable. An important class of mixed constraints consists of combinations of data structures with integer constraints on the size of data structures. Such constraints can express memory safety properties such as absence of memory overflow and out-of-bound array access, which are crucial for program correctness. In this paper we extend the theory of term algebras with the length function which maps a term to its size, resulting in a combined theory of term algebras and Presburger arithmetic. This arithmetic extension provides a natural but tight coupling between the two theories, and hence the general purpose combination methods like Nelson-Op-pen combination are not applicable. We present decision procedures for quantifier-free theories in structures with an infinite constant domain and with a finite constant domain. We also present a quantifier elimination procedure for the extended first-order theory that can remove a block of existential quantifiers in one step.