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Formal Methods in System Design

, Volume 31, Issue 2, pp 135–175 | Cite as

On the optimal reachability problem of weighted timed automata

  • Patricia Bouyer
  • Thomas Brihaye
  • Véronique Bruyère
  • Jean-François RaskinEmail author
Article

Abstract

We study the cost-optimal reachability problem for weighted timed automata such that positive and negative costs are allowed on edges and locations. By optimality, we mean an infimum cost as well as a supremum cost. We show that this problem is PSpace-Complete. Our proof uses techniques of linear programming, and thus exploits an important property of optimal runs: their time-transitions use a time τ which is arbitrarily close to an integer. We then propose an extension of the region graph, the weighted discrete graph, whose structure gives light on the way to solve the  cost-optimal reachability problem. We also give an application of the  cost-optimal reachability problem in the context of timed games.

Keywords

Weighted timed automaton Cost-optimal reachability problem 

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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Patricia Bouyer
    • 1
  • Thomas Brihaye
    • 2
  • Véronique Bruyère
    • 2
  • Jean-François Raskin
    • 3
    Email author
  1. 1.LSV–CNRS & ENS de CachanCachanFrance
  2. 2.Faculté des SciencesUniversité de Mons-HainautMonsBelgium
  3. 3.Département d’InformatiqueUniversité Libre de BruxellesBruxellesBelgium

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