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Parsing Linear Context-Free Rewriting Systems with Fast Matrix Multiplication [article]

Shay B. Cohen, Daniel Gildea
2016 arXiv   pre-print
We describe a matrix multiplication recognition algorithm for a subset of binary linear context-free rewriting systems (LCFRS) with running time O(n^ω d) where M(m) = O(m^ω) is the running time for m ×  ...  Our result provides another proof for the best known result for parsing mildly context sensitive formalisms such as combinatory categorial grammars, head grammars, linear indexed grammars, and tree adjoining  ...  Mildly Context-Sensitive Language Recognition Linear context-free rewriting systems fall under the realm of mildly context-sensitive grammar formalisms.  ... 
arXiv:1504.08342v3 fatcat:5uufnpw2wrh35awyt4xtzzyrzq

Supertagging-based Parsing with Linear Context-free Rewriting Systems [article]

Richard Mörbitz, Thomas Ruprecht
2020 arXiv   pre-print
We also describe a modification to usual chart-based LCFRS parsing that accounts for supertagging and introduce a procedure for the transformation of lexical LCFRS derivations into equivalent parse trees  ...  It utilizes neural classifiers and tremendously outperforms previous LCFRS-based parsers in both accuracy and parsing speed.  ...  Linear context-free rewriting systems extend the rule-based string rewriting mechanism of CFG to string tuples; we describe the generation process by compositions.  ... 
arXiv:2010.10238v1 fatcat:cjcmepz5dba2valw7ocy3sbl5e

Efficient parsing with Linear Context-Free Rewriting Systems

Andreas van Cranenburgh
2012 Conference of the European Chapter of the Association for Computational Linguistics  
Previous work on treebank parsing with discontinuous constituents using Linear Context-Free Rewriting systems (LCFRS) has been limited to sentences of up to 30 words, for reasons of computational complexity  ...  There have been some results on binarizing an LCFRS in a manner that minimizes parsing complexity, but the present work shows that parsing long sentences with such an optimally binarized grammar remains  ...  Linear Context-Free Rewriting Systems Linear Context-Free Rewriting Systems (LCFRS; Vijay-Shanker et al., 1987; Weir, 1988) subsume a wide variety of mildly context-sensitive formalisms, such as Tree-Adjoining  ... 
dblp:conf/eacl/Cranenburgh12 fatcat:eobavttysrelfi73t5mp2fughm

Optimal Parsing Strategies for Linear Context-Free Rewriting Systems

Daniel Gildea
2010 North American Chapter of the Association for Computational Linguistics  
Factorization is the operation of transforming a production in a Linear Context-Free Rewriting System (LCFRS) into two simpler productions by factoring out a subset of the nonterminals on the production's  ...  We show how to apply factorization in order to minimize the parsing complexity of the resulting grammar, and study the relationship between rank, fanout, and parsing complexity.  ...  1 Introduction Gómez-Rodríguez et al. (2009a) recently examined the problem of transforming arbitrary grammars in the Linear Context-Free Rewriting System (LCFRS) formalism (Vijay-Shankar et al., 1987  ... 
dblp:conf/naacl/Gildea10 fatcat:y7skdkvxcndzvfj5uy5p7tujeu

Data-Driven Parsing using Probabilistic Linear Context-Free Rewriting Systems

Laura Kallmeyer, Wolfgang Maier
2013 Computational Linguistics  
This paper presents the first efficient implementation of a weighted deductive CYK parser for Probabilistic Linear Context-Free Rewriting Systems (PLCFRSs).  ...  To speed up parsing, we use different context-summary estimates of parse items, some of them allowing for A * parsing. We evaluate our parser with grammars extracted from the German NeGra treebank.  ...  Probabilistic Linear Context-Free Rewriting Systems Definition of PLCFRS LCFRS Definition 1 (LCFRS) A Linear Context-Free Rewriting System (LCFRS) is a tuple N, T, V, P, S where a) N is a finite  ... 
doi:10.1162/coli_a_00136 fatcat:cxqujw5llngrximecgnhjtjdjq

Parsing Linear Context-Free Rewriting Systems with Fast Matrix Multiplication

Shay B. Cohen, Daniel Gildea
2016 Computational Linguistics  
We describe a matrix multiplication recognition algorithm for a subset of binary linear contextfree rewriting systems (LCFRS) with running time O(n ωd ) where M (m) = O(m ω ) is the running time for m  ...  Our result provides another proof for the best known result for parsing mildly context sensitive formalisms such as combinatory categorial grammars, head grammars, linear indexed grammars, and tree adjoining  ...  Mildly Context-Sensitive Language Recognition Linear context-free rewriting systems fall under the realm of mildly context-sensitive grammar formalisms.  ... 
doi:10.1162/coli_a_00254 fatcat:skhanbgkh5e77pxi55cbu5u7ju

Efficient Parsing of Well-Nested Linear Context-Free Rewriting Systems

Carlos Gómez-Rodríguez, Marco Kuhlmann, Giorgio Satta
2010 North American Chapter of the Association for Computational Linguistics  
The use of well-nested linear context-free rewriting systems has been empirically motivated for modeling of the syntax of languages with discontinuous constituents or relatively free word order.  ...  We present a chart-based parsing algorithm that asymptotically improves the known running time upper bound for this class of rewriting systems.  ...  Linear Context-Free Rewriting Systems For the purposes of this paper, a linear context-free rewriting system, henceforth LCFRS, is a construct G = (N, T, P, S), where N is an alphabet of nonterminal symbols  ... 
dblp:conf/naacl/Gomez-RodriguezKS10 fatcat:ifbl63ljl5evfoexnx4q2kifci

Optimal Head-Driven Parsing Complexity for Linear Context-Free Rewriting Systems

Pierluigi Crescenzi, Daniel Gildea, Andrea Marino, Gianluca Rossi, Giorgio Satta
2011 Annual Meeting of the Association for Computational Linguistics  
We study the problem of finding the best headdriven parsing strategy for Linear Context-Free Rewriting System productions.  ...  We show that it is NP-hard to find the best head-driven strategy in terms of either the time or space complexity of parsing.  ...  Introduction Linear Context-Free Rewriting Systems (LCFRSs) (Vijay-Shankar et al., 1987) constitute a very general grammatical formalism which subsumes contextfree grammars (CFGs) and tree adjoining  ... 
dblp:conf/acl/CrescenziGMRS11 fatcat:apdpuo4kojgbbkoezpszuzdkga

Parsing linear context-free rewriting systems

Håkan Burden, Peter Ljunglöf
2005 Proceedings of the Ninth International Workshop on Parsing Technology - Parsing '05   unpublished
We describe four different parsing algorithms for Linear Context-Free Rewriting Systems (Vijay-Shanker et al., 1987) .  ...  In this paper we describe four different parsing algorithms for Linear Context-Free Rewriting Systems. The algorithms are described as deduction systems, and possible optimizations are discussed.  ...  Linear Context-Free Rewriting Systems A linear context-free rewriting system (LCFRS; Vijay-Shanker et al., 1987) is a linear, non-erasing multiple context-free grammar (MCFG; Seki et al., 1991) .  ... 
doi:10.3115/1654494.1654496 fatcat:uizdkgo7hzcj3j6io36i264tti

Supertagging-based Parsing with Linear Context-free Rewriting Systems

Thomas Ruprecht, Richard Mörbitz
2021 Proceedings of the 2021 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies   unpublished
We present the first supertagging-based parser for linear context-free rewriting systems (LCFRS).  ...  We describe a modification to usual chart-based LCFRS parsing that accounts for supertagging and introduce a procedure that transforms lexical LCFRS derivations into equivalent parse trees of the original  ...  Data- driven parsing using probabilistic linear context- free rewriting systems. Computational Linguistics, 39(1):87-119.  ... 
doi:10.18653/v1/2021.naacl-main.232 fatcat:fi5ytsi3wzaq3ggomubdaomc3i

Lexicalization of Probabilistic Linear Context-free Rewriting Systems

Richard Mörbitz, Thomas Ruprecht
2020 Proceedings of the 16th International Conference on Parsing Technologies and the IWPT 2020 Shared Task on Parsing into Enhanced Universal Dependencies   unpublished
We aim for a symbiosis between probabilistic linear context-free rewriting systems (PLCFRS) as a probabilistic grammar formalism and neural models to get the best of both worlds: the interpretability of  ...  Our construction for G preserves the probability assignment and does not increase parsing complexity compared to G.  ...  Linear context-free rewriting systems extend the rule-based string rewriting mechanism of CFG to string tuples; we describe the gener-ation process by compositions.  ... 
doi:10.18653/v1/2020.iwpt-1.10 fatcat:rkobg7n5dndnjkpqj5kb72rgcq

Intersection for Weighted Formalisms

Mark-Jan Nederhof
2011 Finite-State Methods and Natural Language Processing  
context-free rewriting systems (Nederhof and Satta, 2011b).  ...  Prefix probabilities for linear context-free rewriting systems. In Proceed- ings of the 12th International Conference on Parsing Technologies, Dublin, Ireland, October. M.-J. Nederhof and G.  ... 
dblp:conf/fsmnlp/Nederhof11 fatcat:2b3v7awquffdramtv5zp3wknt4

Page 927 of Mathematical Reviews Vol. 54, Issue 3 [page]

1977 Mathematical Reviews  
The covering problem for linear context-free grammars. Theoret. Comput. Sci. 2 (1976), no. 3, 361-382.  ...  LR-parsing of extended context free Acta Informat. 7 (1976), no. 1, 61-73. An extended context-free grammar is a cfg with regular portions written as regular expressions (e.g., A—>a{b}*c|aB).  ... 

Parsing Based on n-Path Tree-Controlled Grammars

Martin Čermák, Jiří Koutný, Alexander Meduna
2011 Theoretical and Applied Informatics  
We deal with restrictions placed on n ≥ 1 paths controlled by a deterministic context-free language, and we recall several basic properties of such a rewriting system.  ...  Then, we study the possibilities of corresponding parsing methods working in polynomial time and demonstrate that some non-context-free languages can be generated by this regulated rewriting model.  ...  As it is demonstrated in Section 4, this generalized rewriting system can generate some languages not captured in the rewriting system introduced in [12] .  ... 
doi:10.2478/v10179-011-0015-7 fatcat:6semipwb7nfdrm5hs5dv4i3c7e

Parsing Without Grammar

Shinsuke Mori, Makoto Nagao
1995 International Workshop/Conference on Parsing Technologies  
\Ve describe and evaluate experimentally a method to parse a tagged corpus without grammar modeling a natural language on context-free language.  ...  Based on these hypotheses, the system finds a set of constituent-like part-of-speech sequences and replaces them with a new symbol.  ...  [Pereira and Schabes, 1992] and [Schabes et al., 1993] proposed a method to infer the parameters of a stochastic context-free grammar from a partially parsed corpus and evaluated the results.  ... 
dblp:conf/iwpt/MoriN95 fatcat:mji3lsg4gzas7l3qrdgepidm6i
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