Skip to main content
SpringerLink
Log in

State Complexity of Concatenation and Complementation of Regular Languages

  • Conference paper
Implementation and Application of Automata (CIAA 2004)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3317))

Included in the following conference series:

Abstract

We investigate the state complexity of concatenation and the nondeterministic state complexity of complementation of regular languages. We show that the upper bounds on the state complexity of concatenation are also tight in the case that the first automaton has more than one accepting state. In the case of nondeterministic state complexity of complementation, we show that the entire range of complexities, up to the known upper bound can be produced.

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.: Intersection and union of regular languages and state complexity. Inform. Process. Lett. 43, 185–190 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  2. 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 

  3. Câmpeanu, C., Culik II, K., Salomaa, K., Yu, S.: State complexity of basic operations on finite languages. In: Boldt, O., Jürgensen, H. (eds.) WIA 1999. LNCS, vol. 2214, pp. 60–70. Springer, Heidelberg (2001)

    Google Scholar 

  4. Câmpeanu, C., Salomaa, K., Yu, S.: Tight lower bound for the state complexity of shuffle of regular languages. J. Autom. Lang. Comb. 7, 303–310 (2002)

    MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  6. Domaratzki, M.: State complexity and proportional removals. J. Autom. Lang. Comb. 7, 455–468 (2002)

    MATH  MathSciNet  Google Scholar 

  7. 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 

  8. Holzer, M., Salomaa, K., Yu, S.: On the state complexity of k-entry deterministic finite automata. J. Autom. Lang. Comb. 6, 453–466 (2001)

    MATH  MathSciNet  Google Scholar 

  9. Holzer, M., Kutrib, M.: State complexity of basic operations on nondeterministic finite automata. In: Champarnaud, J.-M., Maurel, D. (eds.) CIAA 2002. LNCS, vol. 2608, pp. 148–157. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  10. Holzer, M., Kutrib, M.: Unary language operations and their nondeterministic state complexity. In: Ito, M., Toyama, M. (eds.) DLT 2002. LNCS, vol. 2450, pp. 162–172. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

  13. Hromkovič, J.: Descriptional complexity of finite automata: concepts and open problems. J. Autom. Lang. Comb. 7, 519–531 (2002)

    MATH  MathSciNet  Google Scholar 

  14. Hromkovič, J., Seibert, S., Karhumäki, J., Klauck, H., Schnitger, G.: Communication complexity method for measuring nondeterminism in finite automata. Inform. and Comput. 172, 202–217 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  15. Jirásková, G.: Note on minimal automata and uniform communication protocols. In: Martin-Vide, C., Mitrana, V. (eds.) Grammars and Automata for String Processing: From Mathematics and Computer Science to Biology, and Back, pp. 163–170. Taylor and Francis, London (2003)

    Chapter  Google Scholar 

  16. Jirásková, G.: State complexity of some operations on regular languages. In: Csuhaj-Varjú, E., Kintala, C., Wotschke, D., Vaszil, Gy. (eds.) Proc. 5th Workshop Descriptional Complexity of Formal Systems, MTA SZTAKI, Budapest, pp. 114–125 (2003)

    Google Scholar 

  17. Leiss, E.: Succinct representation of regular languages by boolean automata. Theoret. Comput. Sci. 13, 323–330 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  18. Lupanov, O.B.: A comparison of two types of finite automata. Problemy Kibernetiki 9, 321–326 (1963) (in Russian)

    Google Scholar 

  19. Moore, F.R.: On the bounds for state-set size in the proofs of equivalence between deterministic, nondeterministic, and two-way finite automata. IEEE Trans. Comput. 20, 1211–1214 (1971)

    Article  MATH  Google Scholar 

  20. Pighizzini, G.: Unary language concatenation and its state complexity. In: Yu, S., Păun, A. (eds.) CIAA 2000. LNCS, vol. 2088, pp. 252–262. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  21. Pighizzini, G., Shallit, J.: Unary language operations, state complexity and Jacobsthal’s function. Internat. J. Found. Comput. Sci. 13, 145–159 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  22. Rabin, M., Scott, D.: Finite automata and their decision problems. IBM Res. Develop 3, 114–129 (1959)

    Article  MathSciNet  Google Scholar 

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

    Google Scholar 

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

    MATH  Google Scholar 

  25. 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 

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

    Google Scholar 

  27. Yu, S.: A renaissance of automata theory? Bull. Eur. Assoc. Theor. Comput. Sci. EATCS 72, 270–272 (2000)

    Google Scholar 

  28. Yu, S.: State complexity of finite and infinite regular languages. Bull. Eur. Assoc. Theor. Comput. Sci. EATCS 76, 270–272 (2000)

    Google Scholar 

  29. Yu, S.: State complexity of regular languages. J. Autom. Lang. Comb. 6, 221–234 (2001)

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Computer Science, P.J. Šafárik University, Jesenná 5, 040 01, Košice, Slovakia

    Jozef Jirásek & Alexander Szabari

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

    Galina Jirásková & Alexander Szabari

Authors
  1. Jozef Jirásek
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Galina Jirásková
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Alexander Szabari
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Manitoba, R3T 2N2, Winnipeg, MB, Canada

    Michael Domaratzki

  2. Department of Mathematics, University of Turku, Finland

    Alexander Okhotin

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

    Kai Salomaa

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

    Sheng Yu

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Jirásek, J., Jirásková, G., Szabari, A. (2005). State Complexity of Concatenation and Complementation of Regular Languages. In: Domaratzki, M., Okhotin, A., Salomaa, K., Yu, S. (eds) Implementation and Application of Automata. CIAA 2004. Lecture Notes in Computer Science, vol 3317. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30500-2_17

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-30500-2_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-24318-2

  • Online ISBN: 978-3-540-30500-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation