Theory of linear and integer programming
Theory of linear and integer programming
Lifting Propositional Interpolants to the Word-Level
FMCAD '07 Proceedings of the Formal Methods in Computer Aided Design
Program analysis as constraint solving
Proceedings of the 2008 ACM SIGPLAN conference on Programming language design and implementation
InvGen: An Efficient Invariant Generator
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
Counter-example guided predicate abstraction of hybrid systems
TACAS'03 Proceedings of the 9th international conference on Tools and algorithms for the construction and analysis of systems
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
Automatically refining abstract interpretations
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
Efficient generation of craig interpolants in satisfiability modulo theories
ACM Transactions on Computational Logic (TOCL)
Constraint solving for interpolation
Journal of Symbolic Computation
CPACHECKER: a tool for configurable software verification
CAV'11 Proceedings of the 23rd international conference on Computer aided verification
Playing in the grey area of proofs
POPL '12 Proceedings of the 39th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
VMCAI'10 Proceedings of the 11th international conference on Verification, Model Checking, and Abstract Interpretation
Proceedings of the International Conference on Formal Methods in Computer-Aided Design
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
From under-approximations to over-approximations and back
TACAS'12 Proceedings of the 18th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Interpolant strength revisited
SAT'12 Proceedings of the 15th international conference on Theory and Applications of Satisfiability Testing
CAV'12 Proceedings of the 24th international conference on Computer Aided Verification
Leveraging interpolant strength in model checking
CAV'12 Proceedings of the 24th international conference on Computer Aided Verification
UFO: a framework for abstractionand interpolation-based software verification
CAV'12 Proceedings of the 24th international conference on Computer Aided Verification
SAS'12 Proceedings of the 19th international conference on Static Analysis
Symbolic optimization with SMT solvers
Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages
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We describe a compositional approach to Craig interpolation based on the heuristic that simpler proofs of special cases are more likely to generalize. The method produces simple interpolants because it is able to summarize a large set of cases using one relatively simple fact. In particular, we present a method for finding such simple facts in the theory of linear rational arithmetic. This makes it possible to use interpolation to discover inductive invariants for numerical programs that are challenging for existing techniques. We show that in some cases, the compositional approach can also be more efficient than traditional lazy SMT as a decision procedure.