Selected publications at LSV

We introduce perfect half space games, in which the goal of Player 2 is to make the sums of encountered multi-dimensional weights diverge in a direction which is consistent with a chosen sequence of perfect half spaces (chosen dynamically by Player 2). We establish that the bounding games of Jurdzinski et al. (ICALP 2015) can be reduced to perfect half space games, which in turn can be translated to the lexicographic energy games of Colcombet and Niwinski, and are positionally determined in a strong sense (Player 2 can play without knowing the current perfect half space). We finally show how perfect half space games and bounding games can be employed to solve multi-dimensional energy parity games in pseudo-polynomial time when both the numbers of energy dimensions and of priorities are fixed, regardless of whether the initial credit is given as part of the input or existentially quantified. This also yields an optimal 2EXP complexity with given initial credit, where the best known upper bound was non-elementary.

   address = {Reykjavik, Iceland},
   author = {Colcombet, {\relax Th}omas and Jurdzi{\'n}ski, Marcin and Lazi{\'c}, Ranko and Schmitz, Sylvain},
   booktitle = {{P}roceedings of the 32nd {A}nnual {ACM\slash IEEE} {S}ymposium on {L}ogic {I}n {C}omputer {S}cience ({LICS}'17)},
   editor = {Ouaknine, Jo{\"e}l},
   month = jun,
   note = {To appear},
   publisher = {{IEEE} Press},
   title = {Perfect Half Space Games},
   year = {2017},

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