Skip to main content
SpringerLink
Log in

Descriptional Complexity of Nondeterministic Finite Automata

  • Conference paper
Developments in Language Theory (DLT 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4588))

Included in the following conference series:

Abstract

In this talk, I will survey recent results and discuss open problems on the state and transition complexity of nondeterministic finite automata.

Supported by the Natural Sciences and Engineering Research Council of Canada Grant OGP0147224.

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 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Birget, J.-C.: Partial orders on words, minimal elements of regular languages and state complexity. Theoret. Comput. Sci. 119, 267–291 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  2. Domaratzki, M., Salomaa, K.: Transition complexity of language operations. In: Leung, H., Pighizzini, G. (eds.): Proc. of Descriptional Complexity of Formal Systems, DCFS 2006, Las Cruces, NM, pp. 141–152 (2006)

    Google Scholar 

  3. Domaratzki, M., Salomaa, K.: Lower bounds for the transition complexity of NFAs. In: Královič, R., Urzyczyn, P. (eds.) MFCS 2006. LNCS, vol. 4162, pp. 315–326. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  4. Goldstine, J., Kappes, M., Kintala, C.M.R., Leung, H., Malcher, A., Wotschke, D.: Descriptional complexity of machines with limited resources. J. Universal Computer Science 8, 193–234 (2002)

    MathSciNet  Google Scholar 

  5. Glaister, I., Shallit, J.: A lower bound technique for the size of nondeterministic finite automata. Inf. Proc. Letters 59, 75–77 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  6. Gramlich, G., Schnitger, G.: Minimizing NFA’s and regular expressions. In: Diekert, V., Durand, B. (eds.) STACS 2005. LNCS, vol. 3404, pp. 399–411. Springer, Heidelberg (2005)

    Google Scholar 

  7. Gruber, H., Holzer, M.: A note on the number of transitions of nondeterministic finite automata. In: Fernau, H. (ed.) 15. Theorietag der GI-Fachgruppe 0.1.5 Automaten und Formale Sprachen, pp. 24–25 (2005)

    Google Scholar 

  8. Gruber, H., Holzer, M.: Finding lower bounds for nondeterministic state complexity is hard. In: Ibarra, O.H., Dang, Z. (eds.) DLT 2006. LNCS, vol. 4036, pp. 363–374. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  9. Gruber, H., Holzer, M.: Results on the average state complexity of finite automata accepting finite languages. In: Leung, H., Pighizzini, G. (eds.) Proc. of Descriptional Complexity of Formal Systems, DCFS 2006, Las Cruces, NM, pp. 267–275 (2006)

    Google Scholar 

  10. Gruber, H., Holzer, M.: Computational complexity of NFA minimization for finite and unary languages. In: Proc. of 1st International Conference on Language Theory and Applications, LATA (2007)

    Google Scholar 

  11. Gruber, H., Holzer, M.: Inapproximability of nondeterministic state and transition complexity assuming P ≠ NP. In: Proc. of 11th International Conference Developments in Language Theory, DLT (2007)

    Google Scholar 

  12. Holzer, M., Kutrib, M.: Nondeterministic descriptional complexity of regular languages. Internat. J. Foundations of Computer Science 14, 1087–1102 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  13. Hromkovič, J.: Communication Complexity and Parallel Computing. Springer, Heidelberg (1997)

    MATH  Google Scholar 

  14. Hromkovič, J.: Descriptional complexity of finite automata: Concepts and open problems. J. Automata, Languages and Combinatorics 7, 519–531 (2002)

    MATH  Google Scholar 

  15. Jiang, T., Ravikumar, B.: Minimal NFA problems are hard. SIAM J. Computing 22, 1117–1141 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  16. Kari, J.: Personal communication (2006)

    Google Scholar 

  17. Malcher, A.: Minimizing finite automata is computationally hard. Theoret. Comput. Sci. 327, 375–390 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  18. Salomaa, A., Salomaa, K., Yu, S.: State complexity of combined operations. Theoret. Comput. Sci. (to appear)

    Google Scholar 

  19. Salomaa, K., Yu, S.: On the state complexity of combined operations and their estimation. Internat. J. Foundations of Computer Science (to appear)

    Google Scholar 

  20. Schnitger, G.: Regular expressions and NFAs without ε-transitions. In: Durand, B., Thomas, W. (eds.) STACS 2006. LNCS, vol. 3884, pp. 432–443. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  21. Yu, S.: Grail+: A symbolic computation environment for finite-state machines, regular expressions and finite languages (2002), http://www.csd.uwo.ca/Research/grail

  22. Yu, S.: State complexity of regular languages. J. Automata, Languages and Combinatorics 6, 221–234 (2001)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Computing, Queen’s University, Kingston, Ontario K7L 3N6, Canada

    Kai Salomaa

Authors
  1. Kai Salomaa
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Tero Harju Juhani Karhumäki Arto Lepistö

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Salomaa, K. (2007). Descriptional Complexity of Nondeterministic Finite Automata. In: Harju, T., Karhumäki, J., Lepistö, A. (eds) Developments in Language Theory. DLT 2007. Lecture Notes in Computer Science, vol 4588. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73208-2_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-73208-2_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73207-5

  • Online ISBN: 978-3-540-73208-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation