Algebraic Construction of Parsing Schemata

Karl-Michael Schneider


Abstract
We propose an algebraic method for the design of tabular parsing algorithms which uses parsing schemata [7]. The parsing strategy is expressed in a tree algebra. A parsing schema is derived from the tree algebra by means of algebraic operations such as homomorphic images, direct products, subalgebras and quotient algebras. The latter yields a tabular interpretation of the parsing strategy. The proposed method allows simpler and more elegant correctness proofs by using general theorems and is not limited to left-right parsing strategies, unlike current automaton-based approaches. Furthermore, it allows to derive parsing schemata for linear indexed grammars (LIG) from parsing schemata for context-free grammars by means of a correctness preserving algebraic transformation. A new bottom-up head corner parsing schema for LIG is constructed to demonstrate the method.
Anthology ID:
2000.iwpt-1.24
Volume:
Proceedings of the Sixth International Workshop on Parsing Technologies
Month:
February 23-25
Year:
2000
Address:
Trento, Italy
Editors:
Alberto Lavelli, John Carroll, Robert C. Berwick, Harry C. Bunt, Bob Carpenter, John Carroll, Ken Church, Mark Johnson, Aravind Joshi, Ronald Kaplan, Martin Kay, Bernard Lang, Alon Lavie, Anton Nijholt, Christer Samuelsson, Mark Steedman, Oliviero Stock, Hozumi Tanaka, Masaru Tomita, Hans Uszkoreit, K. Vijay-Shanker, David Weir, Mats Wiren
Venue:
IWPT
SIG:
SIGPARSE
Publisher:
Association for Computational Linguistics
Note:
Pages:
242–253
Language:
URL:
https://aclanthology.org/2000.iwpt-1.24
DOI:
Bibkey:
Cite (ACL):
Karl-Michael Schneider. 2000. Algebraic Construction of Parsing Schemata. In Proceedings of the Sixth International Workshop on Parsing Technologies, pages 242–253, Trento, Italy. Association for Computational Linguistics.
Cite (Informal):
Algebraic Construction of Parsing Schemata (Schneider, IWPT 2000)
Copy Citation:
PDF:
https://aclanthology.org/2000.iwpt-1.24.pdf