Automata-Based Symbolic Representations of Polyhedra
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.
KeywordsTransition Relation Explicit State Decision Structure Incidence Relation Boolean Combination
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