Non-erasing variants of the Chomsky---Schützenberger theorem

Authors:
Alexander Okhotin
Affiliations:
Department of Mathematics, University of Turku, Turku, Finland
Venue:
DLT'12 Proceedings of the 16th international conference on Developments in Language Theory
Year:
2012

Citing 6
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Introduction to Formal Language Theory
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The Mathematical Theory of Context-Free Languages

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Abstract

The famous theorem by Chomsky and Schützenberger ("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.