Theory of linear and integer programming
Theory of linear and integer programming
Foundations of logic programming; (2nd extended ed.)
Foundations of logic programming; (2nd extended ed.)
Simplification and elimination of redundant linear arithmetic constraints
Constraint logic programming
Norms on terms and their use in proving universal termination of a logic program
Theoretical Computer Science
PODS '90 Proceedings of the ninth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
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
Possibly Not Closed Convex Polyhedra and the Parma Polyhedra Library
SAS '02 Proceedings of the 9th International Symposium on Static Analysis
A static analyzer for large safety-critical software
PLDI '03 Proceedings of the ACM SIGPLAN 2003 conference on Programming language design and implementation
WCRE '01 Proceedings of the Eighth Working Conference on Reverse Engineering (WCRE'01)
cTI: a constraint-based termination inference tool for ISO-Prolog
Theory and Practice of Logic Programming
Computing convex hulls with a linear solver
Theory and Practice of Logic Programming
Control Generation by Program Transformation
Fundamenta Informaticae - Program Transformation: Theoretical Foundations and Basic Techniques. Part 2
Cartesian factoring of polyhedra in linear relation analysis
SAS'03 Proceedings of the 10th international conference on Static 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
Determinacy inference for logic programs
ESOP'05 Proceedings of the 14th European conference on Programming Languages and Systems
Splitting the Control Flow with Boolean Flags
SAS '08 Proceedings of the 15th international symposium on Static Analysis
A Sound Floating-Point Polyhedra Abstract Domain
APLAS '08 Proceedings of the 6th Asian Symposium on Programming Languages and Systems
Logahedra: A New Weakly Relational Domain
ATVA '09 Proceedings of the 7th International Symposium on Automated Technology for Verification and Analysis
A Note on the Inversion Join for Polyhedral Analysis
Electronic Notes in Theoretical Computer Science (ENTCS)
Speeding up Polyhedral Analysis by Identifying Common Constraints
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
An abstract domain to discover interval linear equalities
VMCAI'10 Proceedings of the 11th international conference on Verification, Model Checking, and Abstract Interpretation
Automatic abstraction for congruences
VMCAI'10 Proceedings of the 11th international conference on Verification, Model Checking, and Abstract Interpretation
Widening polyhedra with landmarks
APLAS'06 Proceedings of the 4th Asian conference on Programming Languages and Systems
The gauge domain: scalable analysis of linear inequality invariants
CAV'12 Proceedings of the 24th international conference on Computer Aided Verification
Taming the wrapping of integer arithmetic
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)
Summarized Dimensions Revisited
Electronic Notes in Theoretical Computer Science (ENTCS)
Polyhedral analysis using parametric objectives
SAS'12 Proceedings of the 19th international conference on Static Analysis
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The intrinsic cost of polyhedra has lead to research on more tractable sub-classes of linear inequalities. Rather than committing to the precision of such a sub-class, this paper presents a projection algorithm that works directly on any sparse system of inequalities and which sacrifices precision only when necessary. The algorithm is based on a novel combination of the Fourier-Motzkin algorithm (for exact projection) and Simplex (for approximate projection). By reformulating the convex hull operation in terms of projection, conversion to the frame representation is avoided altogether. Experimental results conducted on logic programs demonstrate that the resulting analysis is efficient and precise.