  We consider infinite-state Markov decision processes (MDPs) that are induced
by extensions of vector addition systems with states (VASS). Verification
conditions for these MDPs are described by reachability and Buchi objectives
w.r.t. given sets of control-states. We study the decidability of some
qualitative versions of these objectives, i.e., the decidability of whether
such objectives can be achieved surely, almost-surely, or limit-surely. While
most such problems are undecidable in general, some are decidable for large
subclasses in which either only the controller or only the random environment
can change the counter values (while the other side can only change
control-states).
