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International Conference on Developments in Language Theory

DLT 2010: Developments in Language Theory pp 124–135Cite as

On the Hybrid Černý-Road Coloring Problem and Hamiltonian Paths

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6224))

Abstract

The Hybrid Černý-Road coloring problem is investigated for graphs with Hamiltonian paths. We prove that if an aperiodic, strongly connected digraph of costant outdegree with n vertices has an Hamiltonian path, then it admits a synchronizing coloring with a reset word of length 2(n − 2)(n − 1) + 1. The proof is based upon some new results concerning locally strongly transitive automata.

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. 2008” of the University of Rome ”La Sapienza”.

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

    Article  MATH  MathSciNet  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. In: Diekert, V., Nowotka, D. (eds.) DLT 2009. LNCS, vol. 5583, pp. 81–90. Springer, Heidelberg (2009)

    Google Scholar 

  5. Béal, M.-P., Berlinkov, M.V., Perrin, D.: A quadratic upper bound on the size of a synchronizing word in one-cluster automata. International Journal of Foundations of Computer Science (to appear 2010)

    Google Scholar 

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

    MATH  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  8. Carpi, A., D’Alessandro, F.: Strongly transitive automata and the Černý conjecture. Acta Informatica 46, 591–607 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  9. Carpi, A., D’Alessandro, F.: The synchronization problem for locally strongly transitive automata. In: Královič, R., Niwiński, D. (eds.) MFCS 2009. LNCS, vol. 5734, pp. 211–222. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  10. Černý, J.: Poznámka k. homogénnym experimenton s konečnými automatmi. Mat. fyz. cas SAV 14, 208–215 (1964)

    MATH  Google Scholar 

  11. Culik II, K., Karhumäki, J., Kari, J.: A note on synchronized automata and road coloring problem. Internat. J. Found. Comput. Sci. 13, 459–471 (2002)

    Article  MATH  MathSciNet  Google Scholar 

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

    MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

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

    MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    Google Scholar 

  17. 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)

    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. Steinberg, B.: The averaging trick and the Černý conjecture, Preprint arXiv: 0910.0410v2 (2010)

    Google Scholar 

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

    MATH  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.: Communication. In: Around the Černý conjecture, International Workshop, University of Wroclaw, Poland (June 2008)

    Google Scholar 

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

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, via Vanvitelli 1, 06123, Perugia, Italy

    Arturo Carpi

  2. Dipartimento di Matematica, Università di Roma ”La Sapienza”, Piazzale Aldo Moro 2, 00185, Roma, Italy

    Flavio D’Alessandro

  3. Department of Mathematics, Boğaziçi University, 34342, Bebek, Istanbul, Turkey

    Flavio D’Alessandro

Authors
  1. Arturo Carpi
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  2. Flavio D’Alessandro
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Editor information

Editors and Affiliations

  1. Dept. of Computer Science, University of Western Ontario, N6A 5B7, London, ON, Canada

    Yuan Gao , Hanlin Lu , Shinnosuke Seki  & Sheng Yu , ,  & 

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Carpi, A., D’Alessandro, F. (2010). On the Hybrid Černý-Road Coloring Problem and Hamiltonian Paths. In: Gao, Y., Lu, H., Seki, S., Yu, S. (eds) Developments in Language Theory. DLT 2010. Lecture Notes in Computer Science, vol 6224. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14455-4_13

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  • DOI: https://doi.org/10.1007/978-3-642-14455-4_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14454-7

  • Online ISBN: 978-3-642-14455-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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