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
Bibkey:
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)
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PDF:
https://aclanthology.org/2023.eacl-main.52.pdf
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