Synchronizing Automata with a Letter of Deficiency 2

  • D. S. Ananichev
  • M. V. Volkov
  • Yu. I. Zaks
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4036)


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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Ananichev, D.S., Volkov, M.V.: Synchronizing generalized monotonic automata. Theoret. Comput. Sci. 330, 3–13 (2005)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Černý, J.: Poznámka k homogénnym eksperimentom s konecnými automatami (in Slovak). Mat.-Fyz. Cas. Slovensk. Akad. Vied. 14, 208–216 (1964)MATHGoogle Scholar
  3. 3.
    Dubuc, L.: Sur le automates circulaires et la conjecture de Černý (in French). RAIRO Inform. Theor. Appl. 32, 21–34 (1998)MathSciNetGoogle Scholar
  4. 4.
    Eppstein, D.: Reset sequences for monotonic automata. SIAM J. Comput. 19, 500–510 (1990)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Frankl, P.: An extremal problem for two families of sets. Eur. J. Comb. 3, 125–127 (1982)MATHMathSciNetGoogle Scholar
  6. 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)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Kari, J.: Synchronizing finite automata on Eulerian digraphs. Theoret. Comput. Sci. 295, 223–232 (2003)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Mateescu, A., Salomaa, A.: Many-valued truth functions, Černý’s conjecture and road coloring. EATCS Bull. 68, 134–150 (1999)MATHMathSciNetGoogle Scholar
  9. 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. 10.
    Pin, J.-E.: On two combinatorial problems arising from automata theory. Ann. Discrete Math. 17, 535–548 (1983)MATHGoogle Scholar
  11. 11.
    Salomaa, A.: Composition sequences for functions over a finite domain. Theoret. Comput. Sci. 292, 263–281 (2003)MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Trahtman, A.N.: The Černý conjecture for aperiodic automata. J. Automata, Languages and Combinatorics (accepted)Google Scholar
  13. 13.
    Trahtman, A.N.: Noticeable trends and some examples concerning the Černý conjecture (unpublished manuscript)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • D. S. Ananichev
    • 1
  • M. V. Volkov
    • 1
  • Yu. I. Zaks
    • 1
  1. 1.Department of Mathematics and MechanicsUral State UniversityEkaterinburgRussia

Personalised recommendations