This paper deals with the complexity of context-free grammars with 1-letter terminal alphabet. We study the complexity of the membership problem and the inequivalence problem. We show that the first problem is NP-complete and the second one is ΣP2-complete with respect to log-space reduction. The second result also implies that the inequivalence problem is in Pspace, solving an open problem stated by Hunt, Rosenkrantz and Szymanski (1976).
