Fixed-dimensional energy games are in pseudo-polynomial time

Marcin Jurdzinski (1) , Ranko Lazić (2) , Sylvain Schmitz (3)

1 Department of Computer Science [Warwick]
2 University of Warwick [Coventry]
3 LSV - Laboratoire Spécification et Vérification [Cachan]

We generalise the hyperplane separation technique (Chatterjee and Velner, 2013) from multi-dimensional mean-payoff to energy games, and achieve an algorithm for solving the latter whose running time is exponential only in the dimension, but not in the number of vertices of the game graph. This answers an open question whether energy games with arbitrary initial credit can be solved in pseudo-polynomial time for fixed dimensions 3 or larger (Chaloupka, 2013). It also improves the complexity of solving multi-dimensional energy games with given initial credit from non-elementary (Brázdil, Jančar, and Kučera, 2010) to 2EXPTIME, thus establishing their 2EXPTIME-completeness.

Mots clés: energy game; bounding game; first-cycle game; vector addition system

Domaines: Informatique et théorie des jeux [cs.GT]; Logique en informatique [cs.LO]

Marcin Jurdzinski, Ranko Lazić, Sylvain Schmitz. Fixed-dimensional energy games are in pseudo-polynomial time. ICALP 2015: Proceedings of the 42nd International Colloquium on Automata, Languages, and Programming, Jul 2015, Kyoto, Japan. pp.260--272, ⟨10.1007/978-3-662-47666-6_21⟩. ⟨hal-01168300⟩