On the Intersection of Context-Free and Regular Languages
Clemente Pasti, Andreas Opedal, Tiago Pimentel, Tim Vieira, Jason Eisner, Ryan Cotterell
Abstract
The Bar-Hillel construction is a classic result in formal language theory. It shows, by a simple construction, that the intersection of a context-free language and a regular language is itself context-free. In the construction, the regular language is specified by a finite-state automaton. However, neither the original construction (Bar-Hillel et al., 1961) nor its weighted extension (Nederhof and Satta, 2003) can handle finite-state automata with ε-arcs. While it is possible to remove ε-arcs from a finite-state automaton efficiently without modifying the language, such an operation modifies the automaton’s set of paths. We give a construction that generalizes the Bar- Hillel in the case the desired automaton has ε-arcs, and further prove that our generalized construction leads to a grammar that encodes the structure of both the input automaton and grammar while retaining the asymptotic size of the original construction.- Anthology ID:
- 2023.eacl-main.52
- Volume:
- Proceedings of the 17th Conference of the European Chapter of the Association for Computational Linguistics
- Month:
- May
- Year:
- 2023
- Address:
- Dubrovnik, Croatia
- Editors:
- Andreas Vlachos, Isabelle Augenstein
- Venue:
- EACL
- SIG:
- Publisher:
- Association for Computational Linguistics
- Note:
- Pages:
- 737–749
- Language:
- URL:
- https://aclanthology.org/2023.eacl-main.52
- DOI:
- 10.18653/v1/2023.eacl-main.52
- Cite (ACL):
- Clemente Pasti, Andreas Opedal, Tiago Pimentel, Tim Vieira, Jason Eisner, and Ryan Cotterell. 2023. On the Intersection of Context-Free and Regular Languages. In Proceedings of the 17th Conference of the European Chapter of the Association for Computational Linguistics, pages 737–749, Dubrovnik, Croatia. Association for Computational Linguistics.
- Cite (Informal):
- On the Intersection of Context-Free and Regular Languages (Pasti et al., EACL 2023)
- PDF:
- https://preview.aclanthology.org/proper-vol2-ingestion/2023.eacl-main.52.pdf