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|Title:||Self-embedded context-free grammars with regular counterparts|
|Authors:||Andrei, S. |
|Source:||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. https://doi.org/10.1007/s00236-003-0133-8|
|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|
|Appears in Collections:||Staff Publications|
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