Skip to main content

The Synchronization Problem for Locally Strongly Transitive Automata

  • Conference paper
Book cover Mathematical Foundations of Computer Science 2009 (MFCS 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5734))

Abstract

The synchronization problem is investigated for a new class of deterministic automata called locally strongly transitive. An application to synchronizing colorings of aperiodic graphs with a cycle of prime length is also considered.

This work was partially supported by MIUR project “Aspetti matematici e applicazioni emergenti degli automi e dei linguaggi formali” and by fundings “Facoltà di Scienze MM. FF. NN. 2007” of the University of Rome “La Sapienza”.

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

Access this chapter

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  MathSciNet  MATH  Google Scholar 

  2. Ananichev, D.S., Volkov, M.V.: Synchronizing generalized monotonic automata. Theoret. Comput. Sci. 330(1), 3–13 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  3. Béal, M.-P.: A note on Černý’s Conjecture and rational series, technical report, Institut Gaspard Monge, Université de Marne-la-Vallée (2003)

    Google Scholar 

  4. Béal, M.-P., Perrin, D.: A quadratic upper bound on the size of a synchronizing word in one-cluster automata. To appear in the proceedings of Developments in Language Theory, DLT 2009, Stuttgart, Germany (2009)

    Google Scholar 

  5. Berstel, J., Reutenauer, C.: Rational series and their languages. Springer, Heidelberg (1988)

    Book  MATH  Google Scholar 

  6. Carpi, A.: On synchronizing unambiguous automata. Theoret. Comput. Sci. 60, 285–296 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  7. Černý, J., Poznámka, k.: Homogénnym eksperimenton s konečnými automatmi. Mat. Fyz. Cas SAV 14, 208–215 (1964)

    Google Scholar 

  8. Carpi, A., D’Alessandro, F.: The synchronization problem for strongly transitive automata. In: Ito, M., Toyama, M. (eds.) DLT 2008. LNCS, vol. 5257, pp. 240–251. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

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

    MathSciNet  Google Scholar 

  10. Eilenberg, S.: Automata, Languages and Machines, vol. A. Academic Press, London (1974)

    MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    MATH  Google Scholar 

  14. O’ Brien, G.L.: The road coloring problem. Israel J. Math. 39, 145–154 (1981)

    Article  Google Scholar 

  15. Pin, J.E.: Le problème de la synchronization et la conjecture de Cerny, Thèse de 3ème cycle, Université de Paris 6 (1978)

    Google Scholar 

  16. Pin, J.E.: Sur un cas particulier de la conjecture de Cerny. In: Ausiello, G., Böhm, C. (eds.) ICALP 1978. LNCS, vol. 62, pp. 345–352. Springer, Heidelberg (1978)

    Chapter  Google Scholar 

  17. Rystov, I.: Almost optimal bound of recurrent word length for regular automata. Cybern. Syst. Anal. 31(5), 669–674 (1995)

    Article  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  19. Trahtman, A.N.: The road coloring problem. Israel J. Math. (2008) (to appear)

    Google Scholar 

  20. Volkov, M.V.: Communication in: Around the Černý conjecture, International Workshop, University of Wroclaw (Poland) (June 2008)

    Google Scholar 

  21. 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

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Carpi, A., D’Alessandro, F. (2009). The Synchronization Problem for Locally Strongly Transitive Automata. In: Královič, R., Niwiński, D. (eds) Mathematical Foundations of Computer Science 2009. MFCS 2009. Lecture Notes in Computer Science, vol 5734. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03816-7_19

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-03816-7_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03815-0

  • Online ISBN: 978-3-642-03816-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics