Theory of linear and integer programming
Theory of linear and integer programming
Computing the volume, counting integral points, and exponential sums
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
A polynomial time algorithm for counting integral points in polyhedra when the dimension is fixed
Mathematics of Operations Research
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
Finding the exact volume of a polyhedron
Advances in Engineering Software
Cutting planes and the complexity of the integer hull
Cutting planes and the complexity of the integer hull
IBM Journal of Research and Development
Memory optimization by counting points in integer transformations of parametric polytopes
CASES '06 Proceedings of the 2006 international conference on Compilers, architecture and synthesis for embedded systems
A Primal Barvinok Algorithm Based on Irrational Decompositions
SIAM Journal on Discrete Mathematics
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
iB4e: a software framework for parametrizing specialized LP problems
ICMS'06 Proceedings of the Second international conference on Mathematical Software
Experiences with enumeration of integer projections of parametric polytopes
CC'05 Proceedings of the 14th international conference on Compiler Construction
ESOP'05 Proceedings of the 14th European conference 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
Electronic Notes in Theoretical Computer Science (ENTCS)
Quadtrees as an Abstract Domain
Electronic Notes in Theoretical Computer Science (ENTCS)
On the linear ranking problem for integer linear-constraint loops
POPL '13 Proceedings of the 40th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
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Polyhedra are widely used in model checking and abstract interpretation. Polyhedral analysis is effective when the relationships between variables are linear, but suffers from imprecision when it is necessary to take into account the integrality of the represented space. Imprecision also arises when non-linear constraints occur. Moreover, in terms of tractability, even a space defined by linear constraints can become unmanageable owing to the excessive number of inequalities. Thus it is useful to identify those inequalities whose omission has least impact on the represented space. This paper shows how these issues can be addressed in a novel way by growing the integer hull of the space and approximating the number of integral points within a bounded polyhedron.