Skip to main content
SpringerLink
Log in

Slowly Synchronizing Automata and Digraphs

  • Conference paper
Mathematical Foundations of Computer Science 2010 (MFCS 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6281))

Abstract

We present several infinite series of synchronizing automatafor which the minimum length of reset words is close to the square of the number of states. These automata are closely related to primitive digraphs with large exponent.

Supported by the Russian Foundation for Basic Research, grants 09-01-12142 and 10-01-00524, and by the Federal Education Agency of Russia, grant 2.1.1/3537.

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 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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. Adler, R.L., Goodwyn, L.W., Weiss, B.: Equivalence of topological Markov shifts. Israel J. Math. 27, 49–63 (1977)

    Article  MATH  MathSciNet  Google Scholar 

  2. Almeida, J., Steinberg, B.: Matrix mortality and the Černý–Pin conjecture. In: Diekert, V., Nowotka, D. (eds.) Developments in Language Theory. LNCS, vol. 5583, pp. 67–80. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  3. Almeida, M., Moreira, N., Reis, R.: Enumeration and generation with a string automata representation. Theor. Comput. Sci. 387, 93–102 (2007)

    MATH  MathSciNet  Google Scholar 

  4. Ananichev, D.S., Volkov, M.V., Zaks, Y.I.: Synchronizing automata with a letter of deficiency 2. Theor. Comput. Sci. 376, 30–41 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  5. Černý, J.: Poznámka k homogénnym eksperimentom s konečnými automatami. Matematicko-fyzikalny Časopis Slovensk. Akad. Vied 14(3), 208–216 (1964) (in Slovak)

    MATH  Google Scholar 

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

    MathSciNet  Google Scholar 

  7. Dulmage, A.L., Mendelsohn, N.S.: The exponent of a primitive matrix. Can. Math. Bull. 5, 241–244 (1962)

    MATH  MathSciNet  Google Scholar 

  8. Dulmage, A.L., Mendelsohn, N.S.: Gaps in the exponent set of primitive matrices. Ill. J. Math. 8, 642–656 (1964)

    MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  10. 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 

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

    Article  MATH  MathSciNet  Google Scholar 

  12. Pin, J.-E.: Le problème de la synchronization et la conjecture de Černý. Thèse de 3ème cycle. Université de Paris 6 (1978) (in French)

    Google Scholar 

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

    MATH  Google Scholar 

  14. Ramírez Alfonsín, J.L.: The diophantine Frobenius problem. Oxford University Press, Oxford (2005)

    Book  MATH  Google Scholar 

  15. Sandberg, S.: Homing and synchronizing sequences. In: Broy, M., et al. (eds.) Model-Based Testing of Reactive Systems. LNCS, vol. 3472, pp. 5–33. Springer, Heidelberg (2005)

    Google Scholar 

  16. Skvortsov, E., Yu, Z.: Synchronizing random automata. In: Rigo, M. (ed.) AutoMathA 2009, Université de Liège (2009) (submitted)

    Google Scholar 

  17. Trahtman, A.N.: An efficient algorithm finds noticeable trends and examples concerning the Černý conjecture. In: Královič, R., Urzyczyn, P. (eds.) MFCS 2006. LNCS, vol. 4162, pp. 789–800. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  18. Trahtman, A.N.: Notable trends concerning the synchronization of graphs and automata. Electr. Notes Discrete Math. 25, 173–175 (2006)

    Article  MathSciNet  Google Scholar 

  19. Trahtman, A.N.: The Černý conjecture for aperiodic automata. Discrete Math. Theor. Comput. Sci. 9(2), 3–10 (2007)

    MATH  MathSciNet  Google Scholar 

  20. Trahtman, A.N.: Some aspects of synchronization of DFA. J. Comput. Sci. Technol. 23, 719–727 (2008)

    Article  MathSciNet  Google Scholar 

  21. Trahtman, A.N.: The Road Coloring Problem. Israel J. Math. 172, 51–60 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  22. 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 

  23. Volkov, M.V.: Synchronizing automata preserving a chain of partial orders. Theoret. Comput. Sci. 410, 2992–2998 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  24. Wielandt, H.: Unzerlegbare, nicht negative Matrizen. Math. Z. 52, 642–648 (1950) (in German)

    Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Dmitry Ananichev, Vladimir Gusev & Mikhail Volkov

Authors
  1. Dmitry Ananichev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Vladimir Gusev
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mikhail Volkov
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Falculty of Informatics, Masaryk University, Botanicka 68a, 602 00, Brno, Czech Republic

    Petr Hliněný

  2. Faculty of Informatics, Masaryk University, Botanicka 68a, 602 00, Brno, Czech Republic

    Antonín Kučera

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Ananichev, D., Gusev, V., Volkov, M. (2010). Slowly Synchronizing Automata and Digraphs. In: Hliněný, P., Kučera, A. (eds) Mathematical Foundations of Computer Science 2010. MFCS 2010. Lecture Notes in Computer Science, vol 6281. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15155-2_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-15155-2_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15154-5

  • Online ISBN: 978-3-642-15155-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation