Skip to main content
Springer Nature Link
Log in

Universal Witnesses for State Complexity of Boolean Operations and Concatenation Combined with Star

  • Conference paper
Descriptional Complexity of Formal Systems (DCFS 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8031))

Included in the following conference series:

Abstract

We study the state complexity of boolean operations and product (concatenation, catenation) combined with star. We derive tight upper bounds for the symmetric differences and differences of two languages, one or both of which are starred, and for the product of two starred languages. We prove that the previously discovered bounds for the union and the intersection of languages with one or two starred arguments, for the product of two languages one of which is starred, and for the star of the product of two languages, can all be met by the recently introduced universal witnesses and their variants.

This work was supported by the Natural Sciences and Engineering Research Council of Canada under grant No. OGP0000871, and was done while the second author was at the University of Waterloo.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

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.

Similar content being viewed by others

References

  1. Brzozowski, J.: Quotient complexity of regular languages. J. Autom. Lang. Comb. 15(1/2), 71–89 (2010)

    Google Scholar 

  2. Brzozowski, J.: In search of most complex regular languages. In: Moreira, N., Reis, R. (eds.) CIAA 2012. LNCS, vol. 7381, pp. 5–24. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  3. Brzozowski, J., Liu, D.: Universal witnesses for state complexity of basic operations combined with reversal (July 2012), http://arxiv.org/abs/1207.0535

  4. Brzozowski, J., Liu, D.: Universal witnesses for state complexity of boolean operations and concatenation combined with star (July 2012), http://arxiv.org/abs/1207.1982

  5. Cui, B., Gao, Y., Kari, L., Yu, S.: State complexity of combined operations with two basic operations. Theoret. Comput. Sci. 437, 82–102 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  6. Cui, B., Gao, Y., Kari, L., Yu, S.: State complexity of two combined operations: catenation-star and catenation-reversal. Int. J. Found. Comput. Sc. 23(1), 51–66 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  7. Gao, Y., Kari, L., Yu, S.: State complexity of union and intersection of star on k regular languages. Theoret. Comput. Sci. 429, 98–107 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  8. Gao, Y., Salomaa, K., Yu, S.: The state complexity of two combined operations: star of catenation and star of reversal. Fund. Inform. 83(1-2), 75–89 (2008)

    MathSciNet  MATH  Google Scholar 

  9. Gao, Y., Yu, S.: State complexity of combined operations with union, intersection, star, and reversal. Fund. Inform. 116, 1–14 (2012)

    MathSciNet  Google Scholar 

  10. Jirásková, G., Okhotin, A.: On the state complexity of star of union and star of intersection. Fund. Inform. 109, 1–18 (2011)

    MathSciNet  Google Scholar 

  11. Salomaa, A., Salomaa, K., Yu, S.: State complexity of combined operations. Theoret. Comput. Sci. 383, 140–152 (2007)

    Article  MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, ON, Canada, N2L 3G1

    Janusz Brzozowski

  2. Department of Computer Science, University of Toronto, Toronto, ON, Canada, M5S 3G4

    David Liu

Authors
  1. Janusz Brzozowski
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. David Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science, Middlesex College, Western University, N6A 5B7, London, ON, Canada

    Helmut Jurgensen

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

    Rogério Reis

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Brzozowski, J., Liu, D. (2013). Universal Witnesses for State Complexity of Boolean Operations and Concatenation Combined with Star. In: Jurgensen, H., Reis, R. (eds) Descriptional Complexity of Formal Systems. DCFS 2013. Lecture Notes in Computer Science, vol 8031. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39310-5_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-39310-5_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-39309-9

  • Online ISBN: 978-3-642-39310-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics