Theory of linear and integer programming
Theory of linear and integer programming
A practical algorithm for exact array dependence analysis
Communications of the ACM
First-order logic and automated theorem proving (2nd ed.)
First-order logic and automated theorem proving (2nd ed.)
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
Efficient Craig Interpolation for Linear Diophantine (Dis)Equations and Linear Modular Equations
CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
CSIsat: Interpolation for LA+EUF
CAV '08 Proceedings of the 20th international conference on Computer Aided Verification
Interpolants for Linear Arithmetic in SMT
ATVA '08 Proceedings of the 6th International Symposium on Automated Technology for Verification and Analysis
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
Interpolant Generation for UTVPI
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
Constraint solving for interpolation
VMCAI'07 Proceedings of the 8th international conference on Verification, model checking, and abstract interpretation
Lazy abstraction with interpolants
CAV'06 Proceedings of the 18th international conference on Computer Aided Verification
Automatic inference of abstract type behavior
Proceedings of the IEEE/ACM international conference on Automated software engineering
Interpolating quantifier-free Presburger arithmetic
LPAR'10 Proceedings of the 17th international conference on Logic for programming, artificial intelligence, and reasoning
Beyond quantifier-free interpolation in extensions of Presburger arithmetic
VMCAI'11 Proceedings of the 12th international conference on Verification, model checking, and abstract interpretation
Efficient interpolant generation in satisfiability modulo linear integer arithmetic
TACAS'11/ETAPS'11 Proceedings of the 17th international conference on Tools and algorithms for the construction and analysis of systems: part of the joint European conferences on theory and practice of software
On interpolation in decision procedures
TABLEAUX'11 Proceedings of the 20th international conference on Automated reasoning with analytic tableaux and related methods
FroCoS'11 Proceedings of the 8th international conference on Frontiers of combining systems
An Interpolating Sequent Calculus for Quantifier-Free Presburger Arithmetic
Journal of Automated Reasoning
Playing in the grey area of proofs
POPL '12 Proceedings of the 39th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Effective word-level interpolation for software verification
Proceedings of the International Conference on Formal Methods in Computer-Aided Design
Solving recursion-free horn clauses over LI+UIF
APLAS'11 Proceedings of the 9th Asian conference on Programming Languages and Systems
Lazy abstraction with interpolants for arrays
LPAR'12 Proceedings of the 18th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
From strong amalgamability to modularity of quantifier-free interpolation
IJCAR'12 Proceedings of the 6th international joint conference on Automated Reasoning
SMTInterpol: an interpolating SMT solver
SPIN'12 Proceedings of the 19th international conference on Model Checking Software
ATVA'12 Proceedings of the 10th international conference on Automated Technology for Verification and Analysis
Quantifier-free interpolation in combinations of equality interpolating theories
ACM Transactions on Computational Logic (TOCL)
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Craig interpolation has become a versatile tool in formal verification, for instance to generate intermediate assertions for safety analysis of programs. Interpolants are typically determined by annotating the steps of an unsatisfiability proof with partial interpolants. In this paper, we consider Craig interpolation for full quantifier-free Presburger arithmetic (QFPA), for which currently no efficient interpolation procedures are known. Closing this gap, we introduce an interpolating sequent calculus for QFPA and prove it to be sound and complete. We have extended the Princess theorem prover to generate interpolating proofs, and applied it to a large number of publicly available linear integer arithmetic benchmarks. The results indicate the robustness and efficiency of our proof-based interpolation procedure.