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Fast Parsing for Boolean Grammars: A Generalization of Valiant’s Algorithm

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Developments in Language Theory (DLT 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6224))

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Abstract

The well-known parsing algorithm for the context-free grammars due to Valiant (”General context-free recognition in less than cubic time”, Journal of Computer and System Sciences, 10:2 (1975), 308–314) is refactored and generalized to handle the more general Boolean grammars. The algorithm reduces construction of the parsing table to computing multiple products of Boolean matrices of various size. Its time complexity on an input string of length n is \(O(\mathit{BMM}(n) \log n)\), where \(\mathit{BMM}(n)\) is the number of operations needed to multiply two Boolean matrices of size n ×n, which is O(n 2.376) as per the current knowledge.

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Authors and Affiliations

  1. Department of Mathematics, University of Turku, Academy of Finland, Turku, FI-20014, Finland

    Alexander Okhotin

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  1. Alexander Okhotin
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Editor information

Editors and Affiliations

  1. Dept. of Computer Science, University of Western Ontario, N6A 5B7, London, ON, Canada

    Yuan Gao , Hanlin Lu , Shinnosuke Seki  & Sheng Yu , ,  & 

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Okhotin, A. (2010). Fast Parsing for Boolean Grammars: A Generalization of Valiant’s Algorithm. In: Gao, Y., Lu, H., Seki, S., Yu, S. (eds) Developments in Language Theory. DLT 2010. Lecture Notes in Computer Science, vol 6224. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14455-4_31

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  • DOI: https://doi.org/10.1007/978-3-642-14455-4_31

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14454-7

  • Online ISBN: 978-3-642-14455-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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