Exact join detection for convex polyhedra and other numerical abstractions

r Numerical Abstractions6 Roberto Bagnaraa , Patricia M. Hillb , Enea Zaffanellaa aDepartment of Mathematics, University of Parma, Italy bSchool of Computing, University of Leeds, UK Deciding whether the union of two convex polyhedra is a convex polyhedron is a basic problem in polyhedral computation having important applications in the field of constrained control and in the synthesis, analysis, verification and optimization of hardware and software systems. In these application fields, though, general convex polyhedra are only one among many so-called numeriractions: these range from restricted families of (not necessarily closed) convex polyhedra to non-convex geometrical objects. We thus tackle the proban abstract point of view: for a wide range of numerical abstractions that can be modeled as bounded join-semilattices --that is, partial orders where any finite set of elements has a least upper bound--, we show necessary and sufficient conditions for the equivalence between the la...

• Type: Journal
• Year: 2010
• Where: COMGEO
• Authors: Roberto Bagnara, Patricia M. Hill, Enea Zaffanella
• Keywords: Applied Computing, COMGEO 2010, Convex Polyhedra, General Convex Polyhedra, Numerical Abstractions6 Roberto