Skip to main content
SpringerLink
Log in
Book cover

Combinatorics on Words pp 143–153Cite as

Finitely Generated Ideal Languages and Synchronizing Automata

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8079))

Abstract

We study representations of ideal languages by means of strongly connected synchronizing automata. For every finitely generated ideal language L we construct such an automaton with at most 2n states, where n is the maximal length of words in L. Our constructions are based on the De Bruijn graph.

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   54.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   72.00
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. Černý, J.: Poznámka k homogénnym eksperimentom s konečnými automatami. Mat.-Fyz. Cas. Slovensk. Akad. Vied. 14, 208–216 (1964)

    MATH  Google Scholar 

  2. Gusev, V.V., Maslennikova, M.I., Pribavkina, E.V.: Principal ideal languages and synchronizing automata. In: Halava, V., Karhumäki, J., Matiyasevich, Y. (eds.) Proc. of the Second Russian Finnish Symposium on Discrete Mathematics. TUCS Lecture Notes, pp. 79–84 (2012)

    Google Scholar 

  3. Gusev, V.V., Maslennikova, M.I., Pribavkina, E.V.: Principal Ideal languages and synchronizing automata (April 2013), http://arxiv.org/abs/1304.3307

  4. Maslennikova, M.I.: Reset Complexity of Ideal Languages. In: Bieliková, M., Friedrich, G., Gottlob, G., Katzenbeisser, S., Špánek, R., Turán, G. (eds.) Proc. Int. Conf. SOFSEM 2012, vol. II, pp. 33–44. Institute of Computer Science Academy of Sciences of the Czech Republic (2012)

    Google Scholar 

  5. Perrin, D.: Finite automata. In: van Leewen, J. (ed.) Handbook of Theoretical Computer Science, pp. 1–57. Elsevier, B. (1990)

    Google Scholar 

  6. Pribavkina, E., Rodaro, E.: Synchronizing automata with finitely many minimal synchronizing words. Inf. and Comput. 209(3), 568–579 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  7. Pribavkina, E.V., Rodaro, E.: Recognizing synchronizing automata with finitely many minimal synchronizing words is PSPACE-complete. In: Löwe, B., Normann, D., Soskov, I., Soskova, A. (eds.) CiE 2011. LNCS, vol. 6735, pp. 230–238. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  8. Reis, R., Rodaro, E.: Regular Ideal Languages and Synchronizing Automata. In: Karhumäki, J., Lepistö, A., Zamboni, L. (eds.) WORDS 2013. LNCS, vol. 8079, pp. 205–216. Springer, Heidelberg (2013)

    Google Scholar 

  9. Sandberg, S.: Homing and synchronizing sequences. In: Broy, M., Jonsson, B., Katoen, J.-P., Leucker, M., Pretschner, A. (eds.) Model-Based Testing of Reactive Systems. LNCS, vol. 3472, pp. 5–33. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  10. Volkov, M.V.: Synchronizing automata and the Černý conjecture. In: Martín-Vide, C., Otto, F., Fernau, H. (eds.) LATA 2008. LNCS, vol. 5196, pp. 11–27. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Ural Federal University, Ekaterinburg, Russia

    Vladimir V. Gusev, Marina I. Maslennikova & Elena V. Pribavkina

Authors
  1. Vladimir V. Gusev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Marina I. Maslennikova
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Elena V. Pribavkina
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

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

    Juhani Karhumäki

  2. University of Turku, 20014, Turku, Finland

    Arto Lepistö

  3. FUNDIM, University of Turku, Finland

    Luca Zamboni

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Gusev, V.V., Maslennikova, M.I., Pribavkina, E.V. (2013). Finitely Generated Ideal Languages and Synchronizing Automata. In: Karhumäki, J., Lepistö, A., Zamboni, L. (eds) Combinatorics on Words. Lecture Notes in Computer Science, vol 8079. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40579-2_16

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-40579-2_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40578-5

  • Online ISBN: 978-3-642-40579-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation