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
A New Numerical Abstract Domain Based on Difference-Bound Matrices
PADO '01 Proceedings of the Second Symposium on Programs as Data Objects
A Few Graph-Based Relational Numerical Abstract Domains
SAS '02 Proceedings of the 9th International Symposium on Static Analysis
WCRE '01 Proceedings of the Eighth Working Conference on Reverse Engineering (WCRE'01)
Precise and efficient static array bound checking for large embedded C programs
Proceedings of the ACM SIGPLAN 2004 conference on Programming language design and implementation
Pentagons: a weakly relational abstract domain for the efficient validation of array accesses
Proceedings of the 2008 ACM symposium on Applied computing
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
Two variables per linear inequality as an abstract domain
LOPSTR'02 Proceedings of the 12th international conference on Logic based program synthesis and transformation
Interprocedurally analysing linear inequality relations
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
ESOP'05 Proceedings of the 14th European conference on Programming Languages and Systems
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
Program analysis using symbolic ranges
SAS'07 Proceedings of the 14th international conference on Static Analysis
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The inference of linear inequality invariants among variables of a program plays an important role in static analysis. The polyhedral abstract domain introduced by Cousot and Halbwachs in 1978 provides an elegant and precise solution to this problem. However, the computational complexity of higher-dimensional convex hull algorithms makes it impractical for real-size programs. In the past decade, much attention has been devoted to finding efficient alternatives by trading expressiveness for performance. However, polynomial-time algorithms are still too costly to use for large-scale programs, whereas the full expressive power of general linear inequalities is required in many practical cases. In this paper, we introduce the gauge domain, which enables the efficient inference of general linear inequality invariants within loops. The idea behind this domain consists of breaking down an invariant into a set of linear relations between each program variable and all loop counters in scope. Using this abstraction, the complexity of domain operations is no larger than O(kn), where n is the number of variables and k is the maximum depth of loop nests. We demonstrate the effectiveness of this domain on a real 144K LOC intelligent flight control system, which implements advanced adaptive avionics.