An Alternative Construction in Symbolic Reachability Analysis of Second Order Pushdown Systems

Recently, it has been shown that for any higher order pushdown system H and for any regular set C of configurations, the set pre ∗ H(C), is regular. In this paper, we give an alternative proof of this result for second order automata. Our construction of automata for recognizing pre∗H(C) is explicit. The termination of saturation procedure used is obvious. It gives a better bound on size of the automata recognizing pre∗H(C) if there is no alternation present in H and in the automata recognizing C. Using our techniques for two players reachability games on second order pushdown systems, we generalize some result of [2] concerning synthesis of strategies. Analogous to [2], we show two kinds of winning strategies for player 0 and give algorithms to compute them. The first is executable by second order pushdown automata and the second is linear time executable minimum cost strategy.