Complexity of Uniform Membership of Context-Free Tree Grammars

Abstract

We show that the uniform membership problem of context-free tree grammars is PSPACE-complete. The proof of the upper bound is by construction of an equivalent pushdown tree automaton representable in polynomial space. With this technique, we also give an alternative proof that the respective non-uniform membership problem is in NP. A corollary for uniform membership of \(\epsilon \)-free indexed grammars is obtained.