Data structures and algorithms for disjoint set union problems
ACM Computing Surveys (CSUR)
A canonical form for generalized linear constraints
Journal of Symbolic Computation
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
AMAST '02 Proceedings of the 9th International Conference on Algebraic Methodology and Software Technology
Approaches to the Incremental Detection of Implicit Equalities with the Revised Simplex Method
PLILP '98/ALP '98 Proceedings of the 10th International Symposium on Principles of Declarative Programming
Not necessarily closed convex polyhedra and the double description method
Formal Aspects of Computing
Some ways to reduce the space dimension in polyhedra computations
Formal Methods in System Design
Value-Range Analysis of C Programs: Towards Proving the Absence of Buffer Overflow Vulnerabilities
Value-Range Analysis of C Programs: Towards Proving the Absence of Buffer Overflow Vulnerabilities
A combination framework for tracking partition sizes
Proceedings of the 36th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Exploiting sparsity in polyhedral analysis
SAS'05 Proceedings of the 12th international conference on Static Analysis
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Sets of linear inequalities are an expressive reasoning tool for approximating the reachable states of a program. However, the most precise way to join two states is to calculate the convex hull of the two polyhedra that are represented by the inequality sets, an operation that is exponential in the dimension of the polyhedra. We investigate how similarities in the two input polyhedra can be exploited to improve the performance of this costly operation. In particular, we discuss how common equalities and certain inequalities can be omitted from the calculation without affecting the result. We expose a maximum of common equalities and inequalities by converting the polyhedra into a normal form and give experimental evidence of the merit of our method.