Final Sentential Forms
Tom\'a\v{s} Ko\v{z}\'ar, Zbyn\v{e}k K\v{r}ivka, Alexander Meduna

TL;DR
This paper explores the properties of final sentential forms in context-free grammars, establishing conditions under which their final languages are context-free or recursively enumerable, with implications for language classification.
Contribution
It introduces the concept of final sentential forms and characterizes the languages generated by context-free grammars finalized by regular or specific recursively enumerable languages.
Findings
Languages finalized by regular languages are context-free.
Existence of propagating grammars characterizes recursively enumerable languages.
Final forms relate to language classification and computational properties.
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
