Skip to main content
SpringerLink
Log in
Book cover

International Workshop on Descriptional Complexity of Formal Systems

DCFS 2014: Descriptional Complexity of Formal Systems pp 222–233Cite as

Complement on Prefix-Free, Suffix-Free, and Non-Returning NFA Languages

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8614))

Abstract

We prove that the tight bound on the nondeterministic state complexity of complementation on prefix-free and suffix-free languages is 2n − 1. To prove tightness, we use a ternary alphabet, and we show that this bound cannot be met by any binary prefix-free language. On non-returning languages, the upper bound is 2n − 1 + 1, and it is tight already in the binary case. We also study the unary case in all three classes.

This is a preview of subscription content, 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aho, A.V., Ullman, J.D., Yannakakis, M.: On notions of information transfer in VLSI circuits. In: Johnson, D.S., et al. (eds.) STOC 1983, pp. 133–139. ACM (1983)

    Google Scholar 

  2. Bach, E., Shallit, J.: 2.7 in Algorithmic Number Theory. Efficient Algorithms, vol. 1. MIT Press, Cambridge (1996)

    Google Scholar 

  3. Birget, J.C.: Partial orders on words, minimal elements of regular languages, and state complexity. Theoret. Comput. Sci. 119, 267–291 (1993), ERRATUM: Partial orders on words, minimal elements of regular languages, and state complexity (2002), http://clam.rutgers.edu/~birget/papers.html

  4. Chrobak, M.: Finite automata and unary languages. Theoret. Comput. Sci. 47, 149–158 (1986)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  6. Eom, H.-S., Han, Y.-S., Jirásková, G.: State complexity of basic operations on non-returning regular languages. In: Jurgensen, H., Reis, R. (eds.) DCFS 2013. LNCS, vol. 8031, pp. 54–65. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  7. Ellul, K.: Descriptional complexity measures of regular languages. Master’s thesis. University of Waterloo (2002)

    Google Scholar 

  8. Han, Y.-S., Salomaa, K.: State complexity of basic operations on suffix-free regular languages. Theoret. Comput. Sci. 410, 2537–2548 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  9. Han, Y.-S., Salomaa, K., Wood, D.: Operational state complexity of prefix-free regular languages. In: Automata, Formal Languages, and Related Topics, pp. 99–115. Institute of Informatics, University of Szeged (2009)

    Google Scholar 

  10. Han, Y.-S., Salomaa, K., Wood, D.: Nondeterministic state complexity of basic operations for prefix-free regular languages. Fundam. Inform. 90, 93–106 (2009)

    MATH  MathSciNet  Google Scholar 

  11. Han, Y.-S., Salomaa, K.: Nondeterministic state complexity for suffix-free regular languages. In: McQuillan, I., Pighizzini, G. (eds.) DCFS 2010. EPTCS, vol. 31, pp. 189–196 (2010)

    Google Scholar 

  12. Holzer, M., Kutrib, M.: Nondeterministic descriptional complexity of regular languages. Int. J. Found. Comput. Sci. 14, 1087–1102 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  13. Hromkovič, J.: Communication complexity and parallel computing. Springer (1997)

    Google Scholar 

  14. Jirásková, G.: State complexity of some operations on regular languages. In: Csuhaj-Varjú, E., et al. (eds.) DCFS 2003. MTA SZTAKI, pp. 114–125. Hungarian Academy of Sciences, Budapest (2003)

    Google Scholar 

  15. Jirásková, G.: State complexity of some operations on binary regular languages. Theoret. Comput. Sci. 330, 287–298 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  16. Maslov, A.N.: Estimates of the number of states of finite automata. Soviet Math. Doklady 11, 1373–1375 (1970)

    MATH  Google Scholar 

  17. Sakoda, W.J., Sipser, M.: Nondeterminism and the size of two-way finite automata. In: Proc. 10th Annual ACM Symposium on Theory of Computing, pp. 275–286 (1978)

    Google Scholar 

  18. Sipser, M.: Introduction to the theory of computation. PWS Publishing Company, Boston (1997)

    MATH  Google Scholar 

  19. To, A.W.: Unary finite automata vs. arithmetic progressions. Inform. Process. Lett. 109, 1010–1014 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  20. Yu, S.: Regular languages. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages, vol. I, ch. 2, pp. 41–110. Springer, Heidelberg (1997)

    Google Scholar 

  21. Yu, S., Zhuang, Q., Salomaa, K.: The state complexity of some basic operations on regular languages. Theoret. Comput. Sci. 125, 315–328 (1994)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematical Institute, Slovak Academy of Sciences, Grešákova 6, 040 01, Košice, Slovakia

    Galina Jirásková & Peter Mlynárčik

Authors
  1. Galina Jirásková
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Peter Mlynárčik
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science, The University of Western Ontario, N6A 5B7, London, Ontario, Canada

    Helmut Jürgensen

  2. Department of Mathematics and TUCS, University of Turku, 20014, Turku, Finland

    Juhani Karhumäki

  3. University of Turku, Fi-20014, Turku, Finland

    Alexander Okhotin

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Jirásková, G., Mlynárčik, P. (2014). Complement on Prefix-Free, Suffix-Free, and Non-Returning NFA Languages. In: Jürgensen, H., Karhumäki, J., Okhotin, A. (eds) Descriptional Complexity of Formal Systems. DCFS 2014. Lecture Notes in Computer Science, vol 8614. Springer, Cham. https://doi.org/10.1007/978-3-319-09704-6_20

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-09704-6_20

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-09703-9

  • Online ISBN: 978-3-319-09704-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation