Elementary set operations with d-dimensional polyhedra
Proceedings on International Workshop on Computational Geometry on Computational Geometry and its Applications
Symbolic Boolean manipulation with ordered binary-decision diagrams
ACM Computing Surveys (CSUR)
Representations for Rigid Solids: Theory, Methods, and Systems
ACM Computing Surveys (CSUR)
Efficient minimization of deterministic weak &ohgr;-automata
Information Processing Letters
Orthogonal Polyhedra: Representation and Computation
HSCC '99 Proceedings of the Second International Workshop on Hybrid Systems: Computation and Control
An Improved Reachability Analysis Method for Strongly Linear Hybrid Systems (Extended Abstract)
CAV '97 Proceedings of the 9th International Conference on Computer Aided Verification
An n log n algorithm for minimizing states in a finite automaton
An n log n algorithm for minimizing states in a finite automaton
An effective decision procedure for linear arithmetic over the integers and reals
ACM Transactions on Computational Logic (TOCL)
Handbook of Constraint Programming (Foundations of Artificial Intelligence)
Handbook of Constraint Programming (Foundations of Artificial Intelligence)
Computational Geometry: Theory and Applications
A Generalization of Semenov's Theorem to Automata over Real Numbers
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
A fast linear-arithmetic solver for DPLL(T)
CAV'06 Proceedings of the 18th international conference on Computer Aided Verification
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This work describes a data structure, the Implicit Real-Vector Automaton (IRVA), suited for representing symbolically polyhedra, i.e., regions of n-dimensional space defined by finite Boolean combinations of linear inequalities. IRVA can represent exactly arbitrary convex and non-convex polyhedra, including features such as open and closed boundaries, unconnected parts, and non-manifold components. In addition, they provide efficient procedures for deciding whether a point belongs to a given polyhedron, and determining the polyhedron component (vertex, edge, facet, …) that contains a point. An advantage of IRVA is that they can easily be minimized into a canonical form, which leads to a simple and efficient test for equality between represented polyhedra. We also develop an algorithm for computing Boolean combinations of polyhedra represented by IRVA.