Deciding the inequivalence of context-free grammars with 1-letter terminal alphapet is \(\sum ^ p_ 2\)-complete
This paper deals with the computational complexity of two fundamental decision problems for context-free grammars with 1-letter terminal alphabet, namely the membership and inequivalence problems. The main results of this paper are: (1) The membership problem is log-complete for NP, and (2) The inequivalence problem is log-complete for \(\sum^ p_ 2\). In particular, the second result implies that the inequivalence problem for this restricted grammar class is in PSPACE, thereby setting an open question posed by \textit{H. B. Hunt III}, \textit{D. J. Rosenkrantz} and \textit{T. G. Szymanski} [J. Comput. Syst. Sci. 12, 222-268 (1976; Zbl 0334.68044)].
scientific article; zbMATH DE number 3887098