Non-erasing Variants of the Chomsky–Schützenberger Theorem

Abstract

The famous theorem by Chomsky and Schutzenberger (The algebraic theory of context-free languages, 1963) states that every context-free language is representable as h(Dk∩R), where Dk is the Dyck language over $k \geqslant 1$ pairs of brackets, R is a regular language and h is a homomorphism. This paper demonstrates that one can use a non-erasing homomorphism in this characterization, as long as the language contains no one-symbol strings. If the Dyck language is augmented with neutral symbols, the characterization holds for every context-free language using a letter-to-letter homomorphism.