by Jakub Chaloupka, A full version of the paper presented at Workshop on Reachability Problems 2010 August 2010, 36 pages.
FIMU-RS-2010-06. Available as Postscript, PDF.
We consider a two-player infinite game with zero-reachability objectives played on a 2-dimensional vector addition system with states (VASS), the states of which are divided between the two players. Brázdil, Jančar, and Kučera (2010) have shown that for k > 0, deciding the winner in a game on k-dimensional VASS is in