Parsing Linear Context-Free Rewriting Systems with Fast Matrix Multiplication.

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Title:	Parsing Linear Context-Free Rewriting Systems with Fast Matrix Multiplication.
Authors:	Cohen, Shay B.¹ scohen@inf.ed.ac.uk, Gildea, Daniel² gildea@cs.rochester.edu
Source:	Computational Linguistics. Sep2016, Vol. 42 Issue 3, p421-455. 35p.
Subjects:	Parsing (Computer grammar), Rewriting systems (Computer science), Speech perception, Boolean matrices, Matrix multiplications, Computational linguistics
Abstract:	We describe a recognition algorithm for a subset of binary linear context-free rewriting systems (LCFRS) with running time O(nωd) where M(m) = O(mω) is the running time for m × m matrix multiplication and d is the "contact rank" of the LCFRS-the maximal number of combination and non-combination points that appear in the grammar rules. We also show that this algorithm can be used as a subroutine to obtain a recognition algorithm for general binary LCFRS with running time O(nωd+1). The currently best known ω is smaller than 2.38. 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 grammars, which can be parsed in time O(n4.76). It also shows that inversion transduction grammars can be parsed in time O(n5.76). In addition, binary LCFRS subsumes many other formalisms and types of grammars, for some of which we also improve the asymptotic complexity of parsing. [ABSTRACT FROM AUTHOR]
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Database:	Engineering Source

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Abstract:	We describe a recognition algorithm for a subset of binary linear context-free rewriting systems (LCFRS) with running time O(nωd) where M(m) = O(mω) is the running time for m × m matrix multiplication and d is the "contact rank" of the LCFRS-the maximal number of combination and non-combination points that appear in the grammar rules. We also show that this algorithm can be used as a subroutine to obtain a recognition algorithm for general binary LCFRS with running time O(nωd+1). The currently best known ω is smaller than 2.38. 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 grammars, which can be parsed in time O(n4.76). It also shows that inversion transduction grammars can be parsed in time O(n5.76). In addition, binary LCFRS subsumes many other formalisms and types of grammars, for some of which we also improve the asymptotic complexity of parsing. [ABSTRACT FROM AUTHOR]
ISSN:	08912017
DOI:	10.1162/COLI_a_00254