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arXiv · 2309.08719

Final Sentential Forms

Tomáš Kožár·Zbyněk Křivka·Alexander Meduna
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Abstract

Let G be a context-free grammar with a total alphabet V, and let F be a final language over an alphabet W such that W is a subset of V. A final sentential form is any sentential form of G that, after omitting symbols from V - W, it belongs to F. The string resulting from the elimination of all nonterminals from W in a final sentential form is in the language of G finalized by F if and only if it contains only terminals. The language of any context-free grammar finalized by a regular language is context-free. On the other hand, it is demonstrated that L is a recursively enumerable language if and only if there exists a propagating context-free grammar G such that L equals the language of G finalized by {w#w^R | w is a string over a binary alphabet}, where w^R is the reversal of w.

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Tomáš Kožár, Zbyněk Křivka, Alexander Meduna. 2023-09-15. Final Sentential Forms. https://doi.org/10.4204/eptcs.388.6

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