Regularity in PDA Games Revisited

We study the regularity of sets of winning configurations (winning regions) in countable-state stochastic games played on transition graphs of pushdown automata (PDA games) with reachability objectives. Our main result is proving the regularity of winning regions for qualitative reachability objectives. This completes the classification partially given in a previous paper on this topic. We also improve the upper bounds on the regular representation in cases already solved. We further mention a problem which has also been studied recently: determining the value of a reachability game. Using our methods we prove the regularity of the set of configurations with value 1 and 0.