Skip to main content

A Structural Lemma for Deterministic Context-Free Languages

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 11088)


We present a new structural lemma for deterministic context free languages. From the first sight, it looks like a pumping lemma, because it is also based on iteration properties, but it has significant distinctions that makes it much easier to apply. The structural lemma is a combinatorial analogue of KC-DCF-Lemma (based on Kolmogorov complexity), presented by Li and Vitányi in 1995 and corrected by Glier in 2003. The structural lemma allows not only to prove that a language is not a DCFL, but discloses the structure of DCFLs Myhill-Nerode classes.

A. A. Rubtsov—Supported in part by RFBR grant 16–01–00362. The study has been funded by the Russian Academic Excellence Project ‘5–100’.

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

Buying options

USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-319-98654-8_45
  • 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
USD   79.99
Price excludes VAT (USA)
  • ISBN: 978-3-319-98654-8
  • 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   99.99
Price excludes VAT (USA)


  1. Berstel, J.: Transductions and Context-Free Languages. Teubner Verlag (1979)

    Google Scholar 

  2. Boasson, L.: Un critère de rationnalite des langages algébriques. Automata, Languages. Programming. In: Proc. Sympos. Inst. Rech. Informatique Automatique (IRIA), Rocquencourt, 1972, pp. 359–365 (1973)

    Google Scholar 

  3. Ehrenfeucht, A., Rozenberg, G.: Strong iterative pairs and the regularity of context-free languages. RAIRO. Inform. Théor. 19(1), 43–56 (1985)

    CrossRef  MathSciNet  Google Scholar 

  4. Glier, O.: Kolmogorov complexity and deterministic context-free languages. SIAM J. Comput. 32(5), 1389–1394 (2003)

    CrossRef  MathSciNet  Google Scholar 

  5. Hopcroft, J.E., Ullman, J.D.: Introduction to Automata Theory, Languages and Computation. Addison-Wesley, Boston (1979)

    MATH  Google Scholar 

  6. Li, M., Vitányi, P.: An Introduction to Kolmogorov Complexity and Its Applications. Text and Monographs in Computer Science. Springer, Heidelberg (1993).

    CrossRef  MATH  Google Scholar 

  7. Li, M., Vitányi, P.: A new approach to formal language theory by Kolmogorov complexity. SIAM J. Comput. 24(2), 398–410 (1995)

    CrossRef  MathSciNet  Google Scholar 

  8. Shallit, J.O.: A Second Course in Formal Languages and Automata Theory. Cambridge University Press, Cambridge (2008)

    CrossRef  Google Scholar 

  9. Yu, S.: A pumping lemma for deterministic context-free languages. Inf. Process. Lett. 31(1), 47–51 (1989)

    CrossRef  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Alexander A. Rubtsov .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2018 Springer Nature Switzerland AG

About this paper

Verify currency and authenticity via CrossMark

Cite this paper

Rubtsov, A.A. (2018). A Structural Lemma for Deterministic Context-Free Languages. In: Hoshi, M., Seki, S. (eds) Developments in Language Theory. DLT 2018. Lecture Notes in Computer Science(), vol 11088. Springer, Cham.

Download citation

  • DOI:

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-98653-1

  • Online ISBN: 978-3-319-98654-8

  • eBook Packages: Computer ScienceComputer Science (R0)