/sci/ - Science & Math

Pebble game problem
Input: Directed acyclic graph, vertex V, K pebbles
Allowed elementary steps (no order):
- we can put pebble on vertex X, if in this moment there are pebbles on all vertices from which edge to X exists
- we can take pebble from vertex and put later

Question:
Is there (exists) algorithm (sequence of steps) to put pebble on vertex V ? Prove that this problem is in PSPACE.

I know that this problem can be solved using QBF, but it seems to be complicated. Can someone help ? Thank you.