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Efficient parallel and incremental parsing of practical context-free languages

Part of: JFP Research Articles

Published online by Cambridge University Press:  23 July 2015

JEAN-PHILIPPE BERNARDY  and
KOEN CLAESSEN
JEAN-PHILIPPE BERNARDY
Affiliation:
Chalmers University of Technology & University of Gothenburg, Sweden (e-mail: [email protected], [email protected])
KOEN CLAESSEN
Affiliation:
Chalmers University of Technology & University of Gothenburg, Sweden (e-mail: [email protected], [email protected])
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Abstract

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We present a divide-and-conquer algorithm for parsing context-free languages efficiently. Our algorithm is an instance of Valiant's (1975; General context-free recognition in less than cubic time. J. Comput. Syst. Sci.10(2), 308–314), who reduced the problem of parsing to matrix multiplications. We show that, while the conquer step of Valiant's is O(n3), it improves to O(log2n) under certain conditions satisfied by many useful inputs that occur in practice, and if one uses a sparse representation of matrices. The improvement happens because the multiplications involve an overwhelming majority of empty matrices. This result is relevant to modern computing: divide-and-conquer algorithms with a polylogarithmic conquer step can be parallelized relatively easily.

Type
Articles
Information
Journal of Functional Programming , Volume 25 , 2015 , e10
Copyright
Copyright © Cambridge University Press 2015 

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