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Fast Stochastic Context-Free Parsing: A Stochastic Version of the Valiant Algorithm

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Pattern Recognition and Image Analysis (IbPRIA 2007)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 4477))

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Abstract

In this work, we present a fast stochastic context-free parsing algorithm that is based on a stochastic version of the Valiant algorithm. First, the problem of computing the string probability is reduced to a transitive closure problem. Then, the closure problem is reduced to a matrix multiplication problem of matrices of a special type. Afterwards, some fast algorithm can be used to solve the matrix multiplication problem. Preliminary experiments show that, in practice, an important time savings can be obtained.

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References

  1. Stolcke, A.: An efficient probabilistic context-free parsing algorithm that computes prefix probabilities. Computational Linguistics 21(2), 165–200 (1995)

    MathSciNet  Google Scholar 

  2. Benedí, J., Sánchez, J.: Estimation of stochastic context-free grammars and their use as language models. Computer Speech and Language 19(3), 249–274 (2005)

    Article  Google Scholar 

  3. Ney, H.: Stochastic grammars and pattern recognition. In: Laface, P., Mori, R.D. (eds.) Speech Recognition and Understanding. Recent Advances, pp. 319–344. Springer, Heidelberg (1992)

    Google Scholar 

  4. Sakakibara, Y., Brown, M., Hughey, R., Mian, I., Sjölander, K., Underwood, R., Haussle, D.: The application of stochastic context-free grammars to folding, aligning and modeling homologous rna. Computer and Information Science UCSC-CRL-94-14, Univ. of California, Santa Cruz, CA (1993)

    Google Scholar 

  5. Baker, J.: Trainable grammars for speech recognition. In: Klatt, D.H., Wolf, J.J. (eds.) Speech Communications for the 97th Meeting of the Acoustical Society of America, pp. 31–35. Acoustical Society of America (1979)

    Google Scholar 

  6. Valiant, L.: General context-free recognition in less than cubic time. Journal of computer and system sciences 10, 308–315 (1975)

    MATH  MathSciNet  Google Scholar 

  7. Lee, L.: Fast context-free grammar parsing requires fast boolean matrix multiplication. Journal of the ACM 49(1), 1–15 (2002)

    Article  MathSciNet  Google Scholar 

  8. Rytter, W.: Context-free recognition via shortest paths computation: a version of valiant’s algorithm. Theoretical Computer Science 143, 343–352 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  9. Strassen, V.: Gaussian elimination is not optimal. Numerische Mathematik 13, 354–356 (1969)

    Article  MATH  MathSciNet  Google Scholar 

  10. Coppersmith, D., Winograd, S.: Matrix multiplication via arithmetic progressions. J. Symb. Comput. 9(3), 251–280 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  11. Goodman, J.: Semiring parsing. Computational Linguistics 25(4), 573–605 (1999)

    MathSciNet  Google Scholar 

  12. Harrison, M.: Introduction to Formal Language Theory. Addison-Wesley, London (1978)

    MATH  Google Scholar 

  13. Marcus, M., Santorini, B., Marcinkiewicz, M.: Building a large annotated corpus of english: the penn treebank. Computational Linguistics 19(2), 313–330 (1993)

    Google Scholar 

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Joan Martí José Miguel Benedí Ana Maria Mendonça Joan Serrat

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Benedí, JM., Sánchez, JA. (2007). Fast Stochastic Context-Free Parsing: A Stochastic Version of the Valiant Algorithm. In: Martí, J., Benedí, J.M., Mendonça, A.M., Serrat, J. (eds) Pattern Recognition and Image Analysis. IbPRIA 2007. Lecture Notes in Computer Science, vol 4477. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72847-4_12

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  • DOI: https://doi.org/10.1007/978-3-540-72847-4_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-72846-7

  • Online ISBN: 978-3-540-72847-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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