@article{BouyerBrihayeBruyereRaskin:FMSD:2007,
    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 τwhich 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.},
    Author = {Bouyer, Patricia and Brihaye, Thomas and Bruy{\`e}re, V{\'e}ronique and Raskin, Jean-Fran{\c c}ois},
    File = {On the optimal reachability problem of weighted timed automata - bouyer2007 - a - a - a - q.pdf},
    ISBN = {1572-8102},
    Journal = {Formal Methods in System Design},
    Number = {2},
    Pages = {135--175},
    Title = {On the optimal reachability problem of weighted timed automata},
    URL = {https://doi.org/10.1007/s10703-007-0035-4},
    Volume = {31},
    Year = {2007},
    bdsk-url-1 = {https://doi.org/10.1007/s10703-007-0035-4},
    da = {2007/10/01},
    date-added = {2020-02-06 19:06:38 +0100},
    date-modified = {2020-02-06 19:07:18 +0100},
    file-2 = {Ontheoptimalreachability problem of weighted timed automata - 192ed669b4451741e20f083e4a100942b9d6 - a - a - a - q.pdf},
    id = {Bouyer2007},
    ty = {JOUR},
    doi = {10.1007/s10703-007-0035-4}
}

@article{BouyerBrihayeBruyereRaskin:FMSD:2007, 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 τwhich 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.}, Author = {Bouyer, Patricia and Brihaye, Thomas and Bruy{`e}re, V{\'e}ronique and Raskin, Jean-Fran{\c c}ois}, File = {On the optimal reachability problem of weighted timed automata - bouyer2007 - a - a - a - q.pdf}, ISBN = {1572-8102}, Journal = {Formal Methods in System Design}, Number = {2}, Pages = {135--175}, Title = {On the optimal reachability problem of weighted timed automata}, URL = {https://doi.org/10.1007/s10703-007-0035-4}, Volume = {31}, Year = {2007}, bdsk-url-1 = {https://doi.org/10.1007/s10703-007-0035-4}, da = {2007/10/01}, date-added = {2020-02-06 19:06:38 +0100}, date-modified = {2020-02-06 19:07:18 +0100}, file-2 = {Ontheoptimalreachability problem of weighted timed automata - 192ed669b4451741e20f083e4a100942b9d6 - a - a - a - q.pdf}, id = {Bouyer2007}, ty = {JOUR}, doi = {10.1007/s10703-007-0035-4} }