A canonical form for generalized linear constraints
Journal of Symbolic Computation
Abstract interpretation and application to logic programs
Journal of Logic Programming
A linear algebra framework for static High Performance Fortran code distribution
Scientific Programming - Special issue: High Performance Fortran comes of age
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
Not necessarily closed convex polyhedra and the double description method
Formal Aspects of Computing
Higher-Order and Symbolic Computation
Splitting the Control Flow with Boolean Flags
SAS '08 Proceedings of the 15th international symposium on Static Analysis
Logahedra: A New Weakly Relational Domain
ATVA '09 Proceedings of the 7th International Symposium on Automated Technology for Verification and Analysis
Two variables per linear inequality as an abstract domain
LOPSTR'02 Proceedings of the 12th international conference on Logic based program synthesis and transformation
Scalable analysis of linear systems using mathematical programming
VMCAI'05 Proceedings of the 6th international conference on Verification, Model Checking, and Abstract Interpretation
Trace partitioning in abstract interpretation based static analyzers
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
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
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Linear invariants are essential in many optimization and verification tasks. The domain of convex polyhedra (sets of linear inequalities) has the potential to infer all linear relationships. Yet, it is rarely applied to larger problems due to the join operation whose most precise result is given by the convex hull of two polyhedra which, in turn, may be of exponential size. Recently, Sankaranarayanan et al. proposed an operation called inversion join to efficiently approximate the convex hull. While their proposal has an ad-hoc flavour, we show that it is quite principled and, indeed, complete for planar polyhedra and, for general polyhedra, complete on over 70% of our benchmarks.