### Z-reachability Problem for Games on 2-dimensional Vector Addition Systems with States is in P

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**.

#### Abstract:

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
(k-1)-EXPTIME. In this paper, we show that, for k = 2, the
problem is in P, and thus improve the EXPTIME upper bound.