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. © 2012 Springer-Verlag.
CITATION STYLE
Boigelot, B., Brusten, J., & Degbomont, J. F. (2012). Automata-based symbolic representations of polyhedra. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7183 LNCS, pp. 3–20). https://doi.org/10.1007/978-3-642-28332-1_2
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