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.
CITATION STYLE
Bournez, O., & Maler, O. (2000). On the representation of timed polyhedra. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1853, pp. 793–807). Springer Verlag. https://doi.org/10.1007/3-540-45022-x_66
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