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On the optimal reachability problem of weighted timed automata

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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.

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Author information

Authors and Affiliations

  1. LSV–CNRS & ENS de Cachan, Avenue du Président Wilson 61, 94230, Cachan, France

    Patricia Bouyer

  2. Faculté des Sciences, Université de Mons-Hainaut, Avenue du Champ de Mars 6, 7000, Mons, Belgium

    Thomas Brihaye & Véronique Bruyère

  3. Département d’Informatique, Université Libre de Bruxelles, Boulevard du Triomphe CP 212, 1050, Bruxelles, Belgium

    Jean-François Raskin

Authors
  1. Patricia Bouyer
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  2. Thomas Brihaye
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  3. Véronique Bruyère
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  4. Jean-François Raskin
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Corresponding author

Correspondence to Jean-François Raskin.

Additional information

Research supported by the FRFC project “Centre Fédéré en Vérification” funded by the Belgian National Science Foundation (FNRS) under grant nr 2.4530.02.

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Bouyer, P., Brihaye, T., Bruyère, V. et al. On the optimal reachability problem of weighted timed automata. Form Methods Syst Des 31, 135–175 (2007). https://doi.org/10.1007/s10703-007-0035-4

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