Efficient Symbolic Representation of Convex Polyhedra in High-Dimensional Spaces

  • Bernard Boigelot
  • Isabelle MainzEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11138)


This work is aimed at developing an efficient data structure for representing symbolically convex polyhedra. We introduce an original data structure, the Decomposed Convex Polyhedron (DCP), that is closed under intersection and linear transformations, and allows to check inclusion, equality, and emptiness. The main feature of DCPs lies in their ability to represent concisely polyhedra that can be expressed as combinations of simpler sets, which can overcome combinatorial explosion in high dimensional spaces. DCPs also have the advantage of being reducible into a canonical form, which makes them efficient for representing simple sets constructed by long sequences of manipulations, such as those handled by state-space exploration tools. Their practical efficiency has been evaluated with the help of a prototype implementation, with promising results.



The authors wish to thank Pascal Fontaine and Laurent Poirrier for their precious help in obtaining relevant benchmarks.


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Authors and Affiliations

  1. 1.Institut Montefiore, B28, Université de LiègeLiègeBelgium

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