Skip to main content
SpringerLink
Log in

Synchronizing Automata with a Letter of Deficiency 2

  • Conference paper
Developments in Language Theory (DLT 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4036))

Included in the following conference series:

Abstract

We present two infinite series of synchronizing automata with a letter of deficiency 2 whose shortest reset words are longer than those for synchronizing automata obtained by a straightforward modification of Černý’s construction.

Supported by the Russian Foundation for Basic Research, grant 05-01-00540.

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. Ananichev, D.S., Volkov, M.V.: Synchronizing generalized monotonic automata. Theoret. Comput. Sci. 330, 3–13 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  2. Černý, J.: Poznámka k homogénnym eksperimentom s konecnými automatami (in Slovak). Mat.-Fyz. Cas. Slovensk. Akad. Vied. 14, 208–216 (1964)

    MATH  Google Scholar 

  3. Dubuc, L.: Sur le automates circulaires et la conjecture de Černý (in French). RAIRO Inform. Theor. Appl. 32, 21–34 (1998)

    MathSciNet  Google Scholar 

  4. Eppstein, D.: Reset sequences for monotonic automata. SIAM J. Comput. 19, 500–510 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  5. Frankl, P.: An extremal problem for two families of sets. Eur. J. Comb. 3, 125–127 (1982)

    MATH  MathSciNet  Google Scholar 

  6. Higgins, P.M.: The range order of a product of i transformations from a finite full transformation semigroup. Semigroup Forum 37, 31–36 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  7. Kari, J.: Synchronizing finite automata on Eulerian digraphs. Theoret. Comput. Sci. 295, 223–232 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  8. Mateescu, A., Salomaa, A.: Many-valued truth functions, Černý’s conjecture and road coloring. EATCS Bull. 68, 134–150 (1999)

    MATH  MathSciNet  Google Scholar 

  9. Pin, J.-E.: Le probléme de la synchronisation et la conjecture de Černý (in French). In: De Luca, A. (ed.) Non-commutative Structures in Algebra and Geometric Combinatorics, CNR, Roma. Quaderni de la Ricerca Scientifica, vol. 109, pp. 37–48 (1981)

    Google Scholar 

  10. Pin, J.-E.: On two combinatorial problems arising from automata theory. Ann. Discrete Math. 17, 535–548 (1983)

    MATH  Google Scholar 

  11. Salomaa, A.: Composition sequences for functions over a finite domain. Theoret. Comput. Sci. 292, 263–281 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  12. Trahtman, A.N.: The Černý conjecture for aperiodic automata. J. Automata, Languages and Combinatorics (accepted)

    Google Scholar 

  13. Trahtman, A.N.: Noticeable trends and some examples concerning the Černý conjecture (unpublished manuscript)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Mechanics, Ural State University, 620083, Ekaterinburg, Russia

    D. S. Ananichev, M. V. Volkov & Yu. I. Zaks

Authors
  1. D. S. Ananichev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. V. Volkov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yu. I. Zaks
    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 California, Santa Barbara

    Oscar H. Ibarra

  2. School of Electrical Engineering and Computer Science, Washington State University, WA 99164, Pullman, USA

    Zhe Dang

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Ananichev, D.S., Volkov, M.V., Zaks, Y.I. (2006). Synchronizing Automata with a Letter of Deficiency 2. In: Ibarra, O.H., Dang, Z. (eds) Developments in Language Theory. DLT 2006. Lecture Notes in Computer Science, vol 4036. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11779148_39

Download citation

  • DOI: https://doi.org/10.1007/11779148_39

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-35428-4

  • Online ISBN: 978-3-540-35430-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation