Abstract interpretation and application to logic programs
Journal of Logic Programming
Points-to analysis in almost linear time
POPL '96 Proceedings of the 23rd ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Verification of Real-Time Systems using Linear Relation Analysis
Formal Methods in System Design - Special issue on computer aided verification (CAV 93)
Computing Two-Dimensional Integer Hulls
SIAM Journal on Computing
Ultra-fast aliasing analysis using CLA: a million lines of C code in a second
Proceedings of the ACM SIGPLAN 2001 conference on Programming language design and implementation
Automatic discovery of linear restraints among variables of a program
POPL '78 Proceedings of the 5th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
AMAST '02 Proceedings of the 9th International Conference on Algebraic Methodology and Software Technology
Comparing the Galois Connection and Widening/Narrowing Approaches to Abstract Interpretation
PLILP '92 Proceedings of the 4th International Symposium on Programming Language Implementation and Logic Programming
Polyhedral Analysis for Synchronous Languages
SAS '99 Proceedings of the 6th International Symposium on Static Analysis
Cleanness Checking of String Manipulations in C Programs via Integer Analysis
SAS '01 Proceedings of the 8th International Symposium on Static Analysis
WCRE '01 Proceedings of the Eighth Working Conference on Reverse Engineering (WCRE'01)
Static analysis and computer security: new techniques for software assurance
Static analysis and computer security: new techniques for software assurance
Not necessarily closed convex polyhedra and the double description method
Formal Aspects of Computing
Precise widening operators for convex polyhedra
Science of Computer Programming - Special issue: Static analysis symposium (SAS 2003)
A class of polynomially solvable range constraints for interval analysis without widenings
Theoretical Computer Science - Tools and algorithms for the construction and analysis of systems (TACAS 2004)
Two variables per linear inequality as an abstract domain
LOPSTR'02 Proceedings of the 12th international conference on Logic based program synthesis and transformation
CAV'06 Proceedings of the 18th international conference on Computer Aided Verification
Efficient strongly relational polyhedral analysis
VMCAI'06 Proceedings of the 7th international conference on Verification, Model Checking, and Abstract Interpretation
Exploiting sparsity in polyhedral analysis
SAS'05 Proceedings of the 12th international conference on Static Analysis
Counterexample driven refinement for abstract interpretation
TACAS'06 Proceedings of the 12th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Refining the control structure of loops using static analysis
EMSOFT '09 Proceedings of the seventh ACM international conference on Embedded software
Abstract Fixpoint Computations with Numerical Acceleration Methods
Electronic Notes in Theoretical Computer Science (ENTCS)
Simple and precise widenings for H-polyhedra
APLAS'10 Proceedings of the 8th Asian conference on Programming languages and systems
The two variable per inequality abstract domain
Higher-Order and Symbolic Computation
Numeric bounds analysis with conflict-driven learning
TACAS'12 Proceedings of the 18th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Acceleration of the abstract fixpoint computation in numerical program analysis
Journal of Symbolic Computation
Taming the wrapping of integer arithmetic
SAS'07 Proceedings of the 14th international conference on Static Analysis
Program analysis using symbolic ranges
SAS'07 Proceedings of the 14th international conference on Static Analysis
Stratified Static Analysis Based on Variable Dependencies
Electronic Notes in Theoretical Computer Science (ENTCS)
How to combine widening and narrowing for non-monotonic systems of equations
Proceedings of the 34th ACM SIGPLAN conference on Programming language design and implementation
Abstract acceleration of general linear loops
Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages
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The abstract domain of polyhedra is sufficiently expressive to be deployed in verification. One consequence of the richness of this domain is that long, possibly infinite, sequences of polyhedra can arise in the analysis of loops. Widening and narrowing have been proposed to infer a single polyhedron that summarises such a sequence of polyhedra. Motivated by precision losses encountered in verification, we explain how the classic widening/narrowing approach can be refined by an improved extrapolation strategy. The insight is to record inequalities that are thus far found to be unsatisfiable in the analysis of a loop. These so-called landmarks hint at the amount of widening necessary to reach stability. This extrapolation strategy, which refines widening with thresholds, can infer post-fixpoints that are precise enough not to require narrowing. Unlike previous techniques, our approach interacts well with other domains, is fully automatic, conceptually simple and precise on complex loops.