Theoretical Computer Science
Proceedings of the DIMACS/SYCON workshop on Hybrid systems III : verification and control: verification and control
Proceedings of the DIMACS/SYCON workshop on Hybrid systems III : verification and control: verification and control
Orthogonal polyhedra as geometric bounds in constructive solid geometry
SMA '97 Proceedings of the fourth ACM symposium on Solid modeling and applications
Some Progress in the Symbolic Verification of Timed Automata
CAV '97 Proceedings of the 9th International Conference on Computer Aided Verification
Data-Structures for the Verification of Timed Automata
HART '97 Proceedings of the International Workshop on Hybrid and Real-Time Systems
Algebraic decomposition of non-convex polyhedra
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Interval Diagrams: Increasing Efficiency of Symbolic Real-Time Verification
RTCSA '99 Proceedings of the Sixth International Conference on Real-Time Computing Systems and Applications
Approximation Techniques for Non-linear Problems with Continuum of Solutions
Proceedings of the 5th International Symposium on Abstraction, Reformulation and Approximation
Verification of Timed Automata via Satisfiability Checking
FTRTFT '02 Proceedings of the 7th International Symposium on Formal Techniques in Real-Time and Fault-Tolerant Systems: Co-sponsored by IFIP WG 2.2
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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.