An extension of complex role inclusion axioms in the description logic SROIQ
IJCAR'10 Proceedings of the 5th international conference on Automated Reasoning
Conservative groupoids recognize only regular languages
LATA'12 Proceedings of the 6th international conference on Language and Automata Theory and Applications
SVMAX: a system for secure and valid manipulation of XML data
Proceedings of the 17th International Database Engineering & Applications Symposium
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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.