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.
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Received: 17 January 2003, Published online: 17 February 2004
Stefan Andrei: stefan@infoiasi.ro
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Andrei, S., Chin, WN. & Cavadini, S.V. Self-embedded context-free grammars with regular counterparts. Acta Informatica 40, 349–365 (2004). https://doi.org/10.1007/s00236-003-0133-8
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DOI: https://doi.org/10.1007/s00236-003-0133-8