Static analysis of linear congruence equalities among variables of a program
TAPSOFT '91 Proceedings of the international joint conference on theory and practice of software development on Colloquium on trees in algebra and programming (CAAP '91): vol 1
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
POPL '77 Proceedings of the 4th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Discovering affine equalities using random interpretation
POPL '03 Proceedings of the 30th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
A static analyzer for large safety-critical software
PLDI '03 Proceedings of the ACM SIGPLAN 2003 conference on Programming language design and implementation
Precise interprocedural analysis through linear algebra
Proceedings of the 31st ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Higher-Order and Symbolic Computation
A Sound Floating-Point Polyhedra Abstract Domain
APLAS '08 Proceedings of the 6th Asian Symposium on Programming Languages and Systems
SubPolyhedra: A (More) Scalable Approach to Infer Linear Inequalities
VMCAI '09 Proceedings of the 10th International Conference on Verification, Model Checking, and Abstract Interpretation
Apron: A Library of Numerical Abstract Domains for Static Analysis
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
Interval Polyhedra: An Abstract Domain to Infer Interval Linear Relationships
SAS '09 Proceedings of the 16th International Symposium on Static Analysis
Static analysis by policy iteration on relational domains
ESOP'07 Proceedings of the 16th European conference on Programming
Scalable analysis of linear systems using mathematical programming
VMCAI'05 Proceedings of the 6th international conference on Verification, Model Checking, and Abstract Interpretation
Symbolic methods to enhance the precision of numerical abstract domains
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
Interval slopes as a numerical abstract domain for floating-point variables
SAS'10 Proceedings of the 17th international conference on Static analysis
Simple and precise widenings for H-polyhedra
APLAS'10 Proceedings of the 8th Asian conference on Programming languages and systems
Proceedings of the 19th ACM SIGSOFT symposium and the 13th European conference on Foundations of software engineering
Smoothing a program soundly and robustly
CAV'11 Proceedings of the 23rd international conference on Computer aided verification
Detecting specification errors in declarative languages with constraints
MODELS'12 Proceedings of the 15th international conference on Model Driven Engineering Languages and Systems
Abstract acceleration of general linear loops
Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages
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We introduce a new abstract domain, namely the domain of Interval Linear Equalities (itvLinEqs), which generalizes the affine equality domain with interval coefficients by leveraging results from interval linear algebra. The representation of itvLinEqs is based on a row echelon system of interval linear equalities, which natively allows expressing classical linear relations as well as certain topologically non-convex (even unconnected or non-closed) properties. The row echelon form limits the expressiveness of the domain but yields polynomial-time domain operations. Interval coefficients enable a sound adaptation of itvLinEqs to floating-point arithmetic. itvLinEqs can be used to infer and propagate interval linear constraints, especially for programs involving uncertain or inexact data. The preliminary experimental results are encouraging: itvLinEqs can find a larger range of invariants than the affine equality domain. Moreover, itvLinEqs provides an efficient alternative to polyhedra-like domains.