Logic for computer science: foundations of automatic theorem proving
Logic for computer science: foundations of automatic theorem proving
Assignment Commands with Array References
Journal of the ACM (JACM)
Verification Decidability of Presburger Array Programs
Journal of the ACM (JACM)
A Decision Procedure for the Correctness of a Class of Programs
Journal of the ACM (JACM)
Simplification by Cooperating Decision Procedures
ACM Transactions on Programming Languages and Systems (TOPLAS)
Communications of the ACM
A rewriting approach to satisfiability procedures
Information and Computation - RTA 2001
A Decision Procedure for an Extensional Theory of Arrays
LICS '01 Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science
Model-Theoretic Methods in Combined Constraint Satisfiability
Journal of Automated Reasoning
FroCoS'05 Proceedings of the 5th international conference on Frontiers of Combining Systems
What's decidable about arrays?
VMCAI'06 Proceedings of the 7th international conference on Verification, Model Checking, and Abstract Interpretation
Data structure specifications via local equality axioms
CAV'05 Proceedings of the 17th international conference on Computer Aided Verification
On superposition-based satisfiability procedures and their combination
ICTAC'05 Proceedings of the Second international conference on Theoretical Aspects of Computing
Interpolation and Symbol Elimination
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
On local reasoning in verification
TACAS'08/ETAPS'08 Proceedings of the Theory and practice of software, 14th international conference on Tools and algorithms for the construction and analysis of systems
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The theory of arrays, introduced by McCarthy in his seminal paper “Toward a mathematical science of computation”, is central to Computer Science. Unfortunately, the theory alone is not sufficient for many important verification applications such as program analysis. Motivated by this observation, we study extensions of the theory of arrays whose satisfiability problem (i.e. checking the satisfiability of conjunctions of ground literals) is decidable. In particular, we consider extensions where the indexes of arrays has the algebraic structure of Presburger Arithmetic and the theory of arrays is augmented with axioms characterizing additional symbols such as dimension, sortedness, or the domain of definition of arrays. We provide methods for integrating available decision procedures for the theory of arrays and Presburger Arithmetic with automatic instantiation strategies which allow us to reduce the satisfiability problem for the extension of the theory of arrays to that of the theories decided by the available procedures. Our approach aims to reuse as much as possible existing techniques so to ease the implementation of the proposed methods. To this end, we show how to use both model-theoretic and rewriting-based theorem proving (i.e., superposition) techniques to implement the instantiation strategies of the various extensions.