Regular Strategies In Pushdown Reachability

Abstract. We show that positional winning strategies in pushdown reachability games can be implemented by deterministic nite state au-tomata of exponential size. Such automata read the stack and control state of a given pushdown conguration and output the set of winning moves playable from that position. This result can originally be attributed to Kupferman, Piterman and Vardi using an approach based on two-way tree automata. We present a more direct approach that builds upon the popular saturation technique. Saturation for analysing pushdown systems has been successfully imple-mented by Moped and WALi. Thus, our approach has the potential for practical applications to controller-synthesis problems.