Skip to main content

One-Counter Automata for Parsing and Language Approximation

  • 337 Accesses

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 10977)

Abstract

A grammar characterization of partially blind one-counter languages is presented. One-counter automata are used to build parse trees of the respective grammars. One-counter automata are also used to find the most probable derivations for the stochastic versions of these grammars. Both these tasks are executed in quadratic time in the size of the input. Regular expressions are extended with one-counter language capabilities. Context-free languages are approximated with one-counter languages.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-319-94812-6_25
  • Chapter length: 13 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   59.99
Price excludes VAT (USA)
  • ISBN: 978-3-319-94812-6
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   79.99
Price excludes VAT (USA)

References

  1. Jurafsky, D., Martin, J.H.: Speech and Language Processing, 2nd edn. Prentice-Hall Inc., Upper Saddle River (2009)

    Google Scholar 

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

    CrossRef  MathSciNet  Google Scholar 

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

    CrossRef  Google Scholar 

  4. Petrov, S., Barrett, L., Thibaux, R., Klein, D.: Learning accurate, compact, and interpretable tree annotation. In: Proceedings of the 21st International Conference on Computational Linguistics, pp. 433–440 (2006)

    Google Scholar 

  5. Klein, D., Manning, C.D.: A* parsing: fast exact Viterbi parse selection. In: Proceedings of the 2003 Conference of the North American Chapter of the Association for Computational Linguistics on Human Language Technology - Volume 1, pp. 40–47 (2003)

    Google Scholar 

  6. Autebert, J., Berstel, J., Boasson, L.: Context-free languages and push-down automata. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages. Springer, Heidelberg (1997). https://doi.org/10.1007/978-3-642-59136-5_3

    CrossRef  Google Scholar 

  7. Bouajjani, A., Bozga, M., Habermehl, P., Iosif, R., Moro, P., Vojnar, T.: Programs with lists are counter automata. Formal Methods Syst. Des. 38(2), 158–192 (2011)

    CrossRef  Google Scholar 

  8. Chitic, C., Rosu, D.: On validation of XML streams using finite state machines. In: Proceedings of the 7th International Workshop on the Web and Databases, pp. 85–90 (2004)

    Google Scholar 

  9. Brázdil, T., Brozek, V., Etessami, K., Kucera, A., Wojtczak, D.: One-counter Markov decision processes. In: Proceedings of the 21st Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 863–874 (2010)

    CrossRef  Google Scholar 

  10. Brázdil, T., Brozek, V., Etessami, K.: One-counter stochastic games. In: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, pp. 108–119 (2010)

    Google Scholar 

  11. Etessami, K., Wojtczak, D., Yannakakis, M.: Quasi-birth-death processes, tree-like QBDs, probabilistic 1-counter automata, and pushdown systems. In: 5th International Conference on the Quantitative Evaluation of Systems, pp. 243–253 (2008)

    Google Scholar 

  12. Greibach, S.A.: Remarks on blind and partially blind one-way multicounter machines. Theoret. Comput. Sci. 7, 311–324 (1978)

    CrossRef  MathSciNet  Google Scholar 

  13. Berstel, J.: Transductions and Context-Free Languages. Leitfäden der angewandten Mathematik und Mechanik. Teubner (1979)

    CrossRef  Google Scholar 

  14. Czerwinski, W., Lasota, S.: Regular separability of one counter automata. In: 32nd Annual ACM/IEEE Symposium on Logic in Computer Science, pp. 1–12 (2017)

    Google Scholar 

  15. Render, E., Kambites, M.: Polycyclic and bicyclic valence automata. In: Martín-Vide, C., Otto, F., Fernau, H. (eds.) LATA 2008. LNCS, vol. 5196, pp. 464–475. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-88282-4_42

    CrossRef  MATH  Google Scholar 

  16. Brandenburg, F.J.: On the intersection of stacks and queues. Theoret. Comput. Sci. 58(1), 69–80 (1988)

    CrossRef  MathSciNet  Google Scholar 

  17. Mohri, M., Nederhof, M.J.: Regular approximation of context-free grammars through transformation. In: Junqua, J.C., van Noord, G. (eds.) Robustness in Language and Speech Technology. Text, Speech and Language Technology, pp. 153–163. Springer, Dordrecht (2001). https://doi.org/10.1007/978-94-015-9719-7_6

    CrossRef  Google Scholar 

  18. Eğecioğlu, Ö.: Strongly regular grammars and regular approximation of context-free languages. In: Developments in Language Theory: 13th International Conference, pp. 207–220 (2009)

    CrossRef  Google Scholar 

  19. Sakharov, A., Sakharov, T.: The Viterbi algorithm for subsets of stochastic context-free languages. Inf. Process. Lett. 135, 68–72 (2018)

    CrossRef  MathSciNet  Google Scholar 

  20. Friedl, J.E.F.: Mastering Regular Expressions. O’Reilly & Associates Inc., Sebastopol (2002)

    MATH  Google Scholar 

  21. Hromkovič, J., Seibert, S., Wilke, T.: Translating regular expressions into small \(\epsilon \)-free nondeterministic finite automata. J. Comput. Syst. Sci. 62(4), 565–588 (2001)

    CrossRef  MathSciNet  Google Scholar 

  22. Cotter, A., Gupta, M.R., Pfeifer, J.: A light touch for heavily constrained SGD. In: Proceedings of the 29th Conference on Learning Theory, pp. 729–771 (2016)

    Google Scholar 

  23. Grathwohl, N.B.B., Henglein, F., Rasmussen, U.T.: Optimally streaming greedy regular expression parsing. In: International Conference on Theoretical Aspects of Computing, pp. 224–240 (2014)

    Google Scholar 

  24. Nederhof, M.J.: Context-free parsing through regular approximation. In: Proceedings of the International Workshop on Finite State Methods in Natural Language Processing, pp. 13–24 (1998)

    Google Scholar 

  25. Nederhof, M.J.: A general technique to train language models on language models. Comput. Linguist. 31(2), 173–186 (2005)

    CrossRef  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Alexander Sakharov .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this paper

Verify currency and authenticity via CrossMark

Cite this paper

Sakharov, A. (2018). One-Counter Automata for Parsing and Language Approximation. In: Câmpeanu, C. (eds) Implementation and Application of Automata. CIAA 2018. Lecture Notes in Computer Science(), vol 10977. Springer, Cham. https://doi.org/10.1007/978-3-319-94812-6_25

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-94812-6_25

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-94811-9

  • Online ISBN: 978-3-319-94812-6

  • eBook Packages: Computer ScienceComputer Science (R0)