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Strongly transitive automata and the Černý conjecture

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Abstract

The synchronization problem is investigated for a new class of deterministic automata called strongly transitive. An extension to unambiguous automata is also considered.

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

  3. Béal M.P., Czeizler E., Kari J., Perrin D.: Unambiguous automata. Math. Comput. Sci. 1, 625–638 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  4. Berstel J., Reutenauer C.: Rational Series and Their Languages. Springer, Berlin (1988)

    MATH  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  6. Carpi A., D’Alessandro F.: The synchronization problem for strongly transitive automata. In: Ito, M., Toyama, M. (eds) Developments in Language Theory, DLT 2008, Lecture Notes in Computer Science, vol. 5257, Springer, Berlin (2008)

    Google Scholar 

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

    MATH  Google Scholar 

  8. Césari Y.: Sur l’application du théorème de Suschkewitsch à l’étude des codes rationnels complets. In: Loeckx, J. (eds) Automata, Languages and Programming, Lecture Notes in Computer Science, vol. 14, pp. 342–350. Springer, Berlin (1974)

    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, New York (1974)

    MATH  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    MATH  MathSciNet  Google Scholar 

  13. Goralč P., Hedrlín Z., Koubek V., Ryšlinková J.: A game of composing binary relations. RAIRO Inform. Théor. 16, 365–369 (1982)

    MATH  Google Scholar 

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

    Article  MATH  MathSciNet  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)

  16. Pin, J.E.: Sur un cas particulier de la conjecture de Cerny, In: Proceedings of the 5th ICALP. Lecture Notes in Computer Science, vol. 62, pp. 345–352. Springer, Berlin (1978)

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

    MATH  Google Scholar 

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

    Article  Google Scholar 

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

    MATH  MathSciNet  Google Scholar 

  20. Volkov, M.V.: Synchronizing automata and the Černý conjecture. In: Martín-Vide, C., Otto, F., Fernau, H. (eds.) LATA 2008, Lecture Notes in Computer Science, vol. 5196, pp. 11–27. Springer, Berlin (2008)

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Correspondence to Flavio D’Alessandro.

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This work was partially supported by MIUR project “Linguaggi formali e automi: teoria e applicazioni” and by fundings “Facoltà di Scienze MM. FF. NN. 2006” of the University of Rome “La Sapienza”.

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Carpi, A., D’Alessandro, F. Strongly transitive automata and the Černý conjecture. Acta Informatica 46, 591–607 (2009). https://doi.org/10.1007/s00236-009-0106-7

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  • DOI: https://doi.org/10.1007/s00236-009-0106-7

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