Skip to main content
SpringerLink
Log in

State Complexity of Star and Square of Union of k Regular Languages

  • Conference paper
Descriptional Complexity of Formal Systems (DCFS 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7386))

Included in the following conference series:

Abstract

In this paper, we study the state complexities of \((\bigcup\limits_{i=1}^{k} L_i)^*\) and \((\bigcup\limits_{i=1}^{k} L_i)^2\), where L i , 1 ≤ i ≤ k, k ≥ 2 are regular languages. We obtain exact bounds for both of these multiple combined operations and show that they are much lower than the mathematical compositions of the state complexities of their basic individual component operations, but have similar forms with the state complexities of some participating combined operations.

This research was supported by Natural Science and Engineering Council of Canada Discovery Grant R2824A01, Canada Research Chair Award to L. K.

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. Cui, B., Gao, Y., Kari, L., Yu, S.: State complexity of two combined operations: catenation-star and catenation-reversal. International Journal of Foundations of Computer Science 23(1), 51–56 (2012)

    Article  Google Scholar 

  2. Cui, B., Gao, Y., Kari, L., Yu, S.: State complexity of combined operations with two basic operations. Theoretical Computer Science (2011) (accepted)

    Google Scholar 

  3. Cui, B., Gao, Y., Kari, L., Yu, S.: State complexity of two combined operations: catenation-union and catenation-intersection. International Journal of Foundations of Computer Science 22(8), 1797–1812 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  4. Câmpeanu, C., Culik, 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)

    Chapter  Google Scholar 

  5. Campeanu, C., Salomaa, K., Yu, S.: Tight lower bound for the state complexity of shuffle of regular languages. Journal of Automata, Languages and Combinatorics 7(3), 303–310 (2002)

    MathSciNet  MATH  Google Scholar 

  6. Daley, M., Domaratzki, M., Salomaa, K.: State complexity of orthogonal catenation. In: Proceedings of DCFS 2008, Charlottetown, pp. 134–144 (2008)

    Google Scholar 

  7. Domaratzki, M., Okhotin, A.: State complexity of power. Theoretical Computer Science 410(24-25), 2377–2392 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  8. Ésik, Z., Gao, Y., Liu, G., Yu, S.: Estimation of State Complexity of Combined Operations. Theoretical Computer Science 410(35), 3272–3280 (2008)

    Article  Google Scholar 

  9. Gao, Y., Salomaa, K., Yu, S.: The state complexity of two combined operations: star of catenation and star of Reversal. Fundamenta Informaticae 83(1-2), 75–89 (2008)

    MathSciNet  MATH  Google Scholar 

  10. 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 

  11. Hopcroft, J.E., Motwani, R., Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation, 2nd edn. Addison-Wesley (2001)

    Google Scholar 

  12. Jirásek, J., Jirásková, G., Szabari, A.: State complexity of concatenation and complementation of regular languages. International Journal of Foundations of Computer Science 16, 511–529 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  13. Jirásková, G., Okhotin, A.: On the state complexity of star of union and star of intersection, TUCS Technical Report No. 825 (2007)

    Google Scholar 

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

    MATH  Google Scholar 

  15. Pighizzini, G., Shallit, J.O.: Unary language operations, state complexity and Jacobsthal’s function. IJFCS 13, 145–159 (2002)

    MathSciNet  MATH  Google Scholar 

  16. Rabin, M., Scott, D.: Finite automata and their decision problems. IBM Journal of Research and Development 3(2), 114–125 (1959)

    Article  MathSciNet  Google Scholar 

  17. Rampersad, N.: The state complexity of L 2 and L k. Information Processing Letters 98, 231–234 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  18. Salomaa, A., Salomaa, K., Yu, S.: State complexity of combined operations. Theoretical Computer Science 383, 140–152 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  19. Salomaa, A., Salomaa, K., Yu, S.: Undecidability of the State Complexity of Composed Regular Operations. In: Dediu, A.-H., Inenaga, S., Martín-Vide, C. (eds.) LATA 2011. LNCS, vol. 6638, pp. 489–498. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  20. Yu, S.: State complexity of regular languages. Journal of Automata, Languages and Combinatorics 6(2), 221–234 (2001)

    MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  22. Yu, S.: On the State Complexity of Combined Operations. In: Ibarra, O.H., Yen, H.-C. (eds.) CIAA 2006. LNCS, vol. 4094, pp. 11–22. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Yuan Gao & Lila Kari

Authors
  1. Yuan Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lila Kari
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institut für Informatik, Universität Giessen, Arndtstraße 2, 35392, Giessen, Germany

    Martin Kutrib

  2. Departamento de Ciência de Computadores, Universidade do Porto, Faculdade de Ciências, Rua do Campo Alegre 1021-1055, 4169-007, Porto, Portugal

    Nelma Moreira  & Rogério Reis  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Gao, Y., Kari, L. (2012). State Complexity of Star and Square of Union of k Regular Languages. In: Kutrib, M., Moreira, N., Reis, R. (eds) Descriptional Complexity of Formal Systems. DCFS 2012. Lecture Notes in Computer Science, vol 7386. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31623-4_12

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-31623-4_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31622-7

  • Online ISBN: 978-3-642-31623-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation