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International Colloquium on Automata, Languages, and Programming

ICALP 1979: Automata, Languages and Programming pp 489–497Cite as

On the complexity of general context-free language parsing and recognition

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 71))

Abstract

Several results on the computational complexity of general context-free language parsing and recognition are given. In particular we show that parsing strings of length n is harder than recognizing such strings by a factor of only 0(log n), at most. The same is true for linear and/or unambiguous context-free languages. We also show that the time to multiply \(\sqrt n \times \sqrt n\) Boolean Matrices is a lower bound on the time to recognize all prefixes of a string (or do on-line recognition), which in turn is a lower bound on the time to generate a particular convenient representation of all parses of a string (in an ambiguous grammar). Thus these problems are solvable in linear time only if n×n Boolean matrix multiplication can be done in 0(n2).

This research supported by an IBM pre-doctoral fellowship and by NSF grants GJ-474 and MCS77-02474.

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Authors and Affiliations

  1. Department of Computer Science, University of Washington, 98195, Seattle, Washington, USA

    Walter L. Ruzzo

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  1. Walter L. Ruzzo
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Hermann A. Maurer

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© 1979 Springer-Verlag Berlin Heidelberg

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Ruzzo, W.L. (1979). On the complexity of general context-free language parsing and recognition. In: Maurer, H.A. (eds) Automata, Languages and Programming. ICALP 1979. Lecture Notes in Computer Science, vol 71. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-09510-1_39

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  • DOI: https://doi.org/10.1007/3-540-09510-1_39

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09510-1

  • Online ISBN: 978-3-540-35168-9

  • eBook Packages: Springer Book Archive

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