Variants of Collapsible Pushdown Systems

We analyze the relationship between three ways of generating trees using collapsible pushdown systems (CPS’s): using deterministic CPS’s, nondeterministic CPS’s, and deterministic wordaccepting CPS’s. We prove that (for each level of the CPS and each input alphabet) the three classes of trees are equal. The nontrivial translations increase n− 1 times exponentially the size of the level-n CPS. The same results stay true if we restrict ourselves to higher-order pushdown systems without collapse. As a second contribution we prove that the hierarchy of word languages recognized by nondeterministic CPS’s is infinite. This is a consequence of a lemma which bounds the length of the shortest accepting run. It also implies that the hierarchy of ε-closures of configuration graphs is infinite (which was already known). As a side effect we obtain a new algorithm for the reachability problem for CPS’s; it has the same complexity as previously known algorithms. 1998 ACM Subject Classification F.1.1 Models of Computation