Skip to main content
SpringerLink
Log in

Modification of Valiant’s Parsing Algorithm for the String-Searching Problem

  • Conference paper
  • First Online:
Computational Intelligence Methods for Bioinformatics and Biostatistics (CIBB 2019)

Part of the book series: Lecture Notes in Computer Science ((LNBI,volume 12313))

  • 412 Accesses

Abstract

Some string-matching problems can be reduced to parsing: verification whether some sequence can be derived in the given grammar. To apply parser-based solutions to such area as bioinformatics, one needs to improve parsing techniques so that the processing of large amounts of data was possible. The most asymptotically efficient parsing algorithm that can be applied to any context-free grammar is a matrix-based algorithm proposed by Valiant. This paper presents a modification of the Valiant’s algorithm, which facilitates efficient utilization of modern hardware in highly-parallel implementation. Moreover, the modified version significantly decreases the number of excessive computations, accelerating the search of substrings.

The research was supported by the Russian Science Foundation, grant No. 18-11-00100.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    The source code is available on GitHub: https://github.com/SusaninaJulia/PBMM.

References

  1. Albrecht, M., Bard, G., Hart, W.: Algorithm 898. ACM Trans. Math. Softw. 37(1), 1–14 (2010). https://doi.org/10.1145/1644001.1644010

    Article  MATH  Google Scholar 

  2. Arlazarov, V.L., Dinitz, Y.A., Kronrod, M., Faradzhev, I.: On economical construction of the transitive closure of an oriented graph. In: Doklady Akademii Nauk, vol. 194, pp. 487–488. Russian Academy of Sciences (1970)

    Google Scholar 

  3. Dowell, R.D., Eddy, S.R.: Evaluation of several lightweight stochastic context-free grammars for RNA secondary structure prediction. BMC Bioinform. 5(1), 71 (2004)

    Article  Google Scholar 

  4. Durbin, R., Eddy, S., Krogh, A., Mitchison, G.: Biological Sequence Analysis. Cambridge University Press, Cambridge (1996)

    MATH  Google Scholar 

  5. Grigorev., S., Lunina., P.: The composition of dense neural networks and formal grammars for secondary structure analysis. In: Proceedings of the 12th International Joint Conference on Biomedical Engineering Systems and Technologies - Volume 3 BIOINFORMATICS: BIOINFORMATICS, pp. 234–241. INSTICC, SciTePress (2019). https://doi.org/10.5220/0007472302340241

  6. Hopcroft, J.E.: Introduction to Automata Theory, Languages, and Computation. Pearson Education India, Boston (2008)

    Google Scholar 

  7. Kasami, T.: An efficient recognition and syntax-analysis algorithm for context-free languages. Coordinated Science Laboratory Report no. R-257 (1966)

    Google Scholar 

  8. Knudsen, B., Hein, J.: RNA secondary structure prediction using stochastic context-free grammars and evolutionary history. Bioinformatics (Oxford, England) 15(6), 446–454 (1999)

    Article  Google Scholar 

  9. Liu, T., Schmidt, B.: Parallel RNA secondary structure prediction using stochastic context-free grammars. Concurr. Comput. Pract. Exp. 17(14), 1669–1685 (2005)

    Article  Google Scholar 

  10. Okhotin, A.: Conjunctive grammars. J. Autom. Lang. Comb. 6(4), 519–535 (2001)

    MathSciNet  MATH  Google Scholar 

  11. Okhotin, A.: Parsing by matrix multiplication generalized to Boolean grammars. Theor. Comput. Sci. 516, 101–120 (2014). https://doi.org/10.1016/j.tcs.2013.09.011

    Article  MathSciNet  MATH  Google Scholar 

  12. Valiant, L.G.: General context-free recognition in less than cubic time. J. Comput. Syst. Sci. 10(2), 308–315 (1975). https://doi.org/10.1016/S0022-0000(75)80046-8

    Article  MathSciNet  MATH  Google Scholar 

  13. Younger, D.H.: Context-free language processing in time n3. In: Proceedings of the 7th Annual Symposium on Switching and Automata Theory (Swat 1966). SWAT 1966, pp. 7–20. IEEE Computer Society, Washington, DC, USA (1966). https://doi.org/10.1109/SWAT.1966.7

  14. Zier-Vogel, R., Domaratzki, M.: RNA pseudoknot prediction through stochastic conjunctive grammars. In: Computability in Europe 2013. Informal Proceedings, pp. 80–89 (2013)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Saint Petersburg State University, Universitetskaya nab. 7/9, St. Petersburg, 199034, Russia

    Yuliya Susanina, Anna Yaveyn & Semyon Grigorev

  2. JetBrains Research, Primorskiy Prospekt 68-70, Building 1, St. Petersburg, 197374, Russia

    Yuliya Susanina & Semyon Grigorev

Authors
  1. Yuliya Susanina
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Anna Yaveyn
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Semyon Grigorev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yuliya Susanina .

Editor information

Editors and Affiliations

  1. University of Bergamo, Bergamo, Italy

    Paolo Cazzaniga

  2. University of Milano-Bicocca, Milan, Italy

    Daniela Besozzi

  3. National Research Council, Segrate, Italy

    Ivan Merelli

  4. Università degli Studi di Trieste, Trieste, Italy

    Luca Manzoni

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Susanina, Y., Yaveyn, A., Grigorev, S. (2020). Modification of Valiant’s Parsing Algorithm for the String-Searching Problem. In: Cazzaniga, P., Besozzi, D., Merelli, I., Manzoni, L. (eds) Computational Intelligence Methods for Bioinformatics and Biostatistics. CIBB 2019. Lecture Notes in Computer Science(), vol 12313. Springer, Cham. https://doi.org/10.1007/978-3-030-63061-4_17

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-63061-4_17

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-63060-7

  • Online ISBN: 978-3-030-63061-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation