On Derivation Trees of Indexed Grammars – An Extension of the uvwxy-Theorem

Abstract

In this paper, the uvwxy-theorem of context-free languages is extended to the case of indexed languages. Applying the extended theorem, it is shown that the finiteness problem for the indexed languages is solvable and certain languages such as $\{a^{n!}\mid n\ge 1\}$ and $\{(\text{\$}w{)}^{|w|}|w\in \{a,b{\}}^{\ast }\}$ are not indexed languages.