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Title: Self-embedded context-free grammars with regular counterparts
Authors: Andrei, S. 
Chin, W.-N. 
Cavadini, S.V.
Issue Date: 2004
Citation: Andrei, S., Chin, W.-N., Cavadini, S.V. (2004). Self-embedded context-free grammars with regular counterparts. Acta Informatica 40 (5) : 349-365. ScholarBank@NUS Repository.
Abstract: In general, it is undecidable if an arbitrary context-free grammar has a regular solution. Past work has focused on special cases, such as one-letter grammars, non self-embedded grammars and the finite-language grammars, for which regular counterparts have been proven to exist. However, little is known about grammars with the self-embedded property. Using systems of equations, we highlight a number of subclasses of grammars, with self-embeddedness terms, such as X \alpha X and \gamma X \gamma , that can still have regular languages as solutions. Constructive proofs that allow these subclasses of context-free grammars to be transformed to regular expressions are provided. We also point out a subclass of context-free grammars that is inherently non-regular. Our latest results can help demarcate more precisely the known boundaries between the regular and non-regular languages, within the context-free domain. © Springer-Verlag 2004.
Source Title: Acta Informatica
ISSN: 00015903
DOI: 10.1007/s00236-003-0133-8
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