Resource Reachability Games on Pushdown Graphs

We consider two-player reachability games with additional resource counters on arenas that are induced by the configuration graphs of pushdown systems. For a play, we define the resource cost to be the highest occurring counter value. In this way, we quantify resources and memory that player 0 needs to win. We introduce the bounded winning problem: Is there a uniform bound k such that player 0 can win the game from a set of initial configurations with this bound k? We provide an effective, saturation-based method to solve this problem for regular sets of initial and goal configurations.