Presburger arithmetic with unary predicates is P11 complete
Journal of Symbolic Logic
First-order logic and automated theorem proving (2nd ed.)
First-order logic and automated theorem proving (2nd ed.)
Simplify: a theorem prover for program checking
Journal of the ACM (JACM)
An interpolating theorem prover
Theoretical Computer Science - Tools and algorithms for the construction and analysis of systems (TACAS 2004)
Interpolation for data structures
Proceedings of the 14th ACM SIGSOFT international symposium on Foundations of software engineering
A Constraint Sequent Calculus for First-Order Logic with Linear Integer Arithmetic
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
Ground Interpolation for the Theory of Equality
TACAS '09 Proceedings of the 15th International Conference on Tools and Algorithms for the Construction and Analysis of Systems: Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2009,
Quantified invariant generation using an interpolating saturation prover
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
VMCAI'10 Proceedings of the 11th international conference on Verification, Model Checking, and Abstract Interpretation
What's decidable about arrays?
VMCAI'06 Proceedings of the 7th international conference on Verification, Model Checking, and Abstract Interpretation
A combination method for generating interpolants
CADE' 20 Proceedings of the 20th international conference on Automated Deduction
An interpolating sequent calculus for quantifier-free presburger arithmetic
IJCAR'10 Proceedings of the 5th international conference on Automated Reasoning
A practical and complete approach to predicate refinement
TACAS'06 Proceedings of the 12th international conference on Tools and Algorithms for the Construction and Analysis of Systems
FroCoS'11 Proceedings of the 8th international conference on Frontiers of combining systems
Playing in the grey area of proofs
POPL '12 Proceedings of the 39th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Proceedings of the International Conference on Formal Methods in Computer-Aided Design
From strong amalgamability to modularity of quantifier-free interpolation
IJCAR'12 Proceedings of the 6th international joint conference on Automated Reasoning
Complete instantiation-based interpolation
POPL '13 Proceedings of the 40th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Proof tree preserving interpolation
TACAS'13 Proceedings of the 19th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Quantifier-free interpolation in combinations of equality interpolating theories
ACM Transactions on Computational Logic (TOCL)
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Craig interpolation has emerged as an effective means of generating candidate program invariants. We present interpolation procedures for the theories of Presburger arithmetic combined with (i) uninterpreted predicates (QPA+UP), (ii) uninterpreted functions (QPA+UF) and (iii) extensional arrays (QPA+AR). We prove that none of these combinations can be effectively interpolated without the use of quantifiers, even if the input formulae are quantifier-free. We go on to identify fragments of QPA+UP and QPA+UF with restricted forms of guarded quantification that are closed under interpolation. Formulae in these fragments can easily be mapped to quantifier-free expressions with integer division. For QPA+AR, we formulate a sound interpolation procedure that potentially produces interpolants with unrestricted quantifiers.