On the Representation of Timed Polyhedra

In this paper we investigate timed polyhedra, i.e. polyhedra which are finite unions of full dimensional simplices of a special kind. Such polyhedra form the basis of timing analysis and in particular of verification tools based on timed automata. We define a representation scheme for these polyhedra based on their extreme vertices, and show that this compact representation scheme is canonical for all (convex and non-convex) polyhedra in any dimension. We then develop relatively efficient algorithms for membership, boolean operations, projection and passage of time for this representation.

• Type: Conference
• Year: 2000
• Where: ICALP
• Authors: Olivier Bournez, Oded Maler
• Keywords: ICALP 2000, Polyhedra, Programming Languages, Representation Scheme, Such Polyhedra Form