Synchronizing Automata Preserving a Chain of Partial Orders

  • Mikhail V. Volkov
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4783)

Abstract

We present a new class of automata which strictly contains the class of aperiodic automata and shares with the latter certain synchronization properties. In particular, every strongly connected automaton in this new class is synchronizing and has a reset word of length \(\left\lfloor\frac{n(n+1)}6\right\rfloor\) where n is the number of states of the automaton.

Keywords

deterministic finite automaton synchronizing automaton Černý conjecture congruence on an automaton weakly monotonic automaton strongly connected automaton 

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References

  1. 1.
    Ananichev, D.S.: The mortality threshold for partially monotonic automata. In: De Felice, C., Restivo, A. (eds.) DLT 2005. LNCS, vol. 3572, pp. 112–121. Springer, Heidelberg (2005)Google Scholar
  2. 2.
    Ananichev, D.S., Volkov, M.V.: Synchronizing generalized monotonic automata. Theoret. Comput. Sci. 330, 3–13 (2005)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Černý, J.: Poznámka k homogénnym eksperimentom s konečnými automatami. Mat.-Fyz. Cas. Slovensk. Akad. Vied. 14, 208–216 (1964) (in Slovak) Google 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.
    Goldberg, K.: Orienting polygonal parts without sensors. Algorithmica 10, 201–225 (1993)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Goralčik, P., Koubek, V.: Rank problems for composite transformations. Algebra and Computation 5, 309–316 (1995)CrossRefGoogle 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.
    McNaughton, R., Papert, S.A.: Counter-free automata. MIT Press, Cambridge (1971)MATHGoogle 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.
    Rystsov, I.: Reset words for commutative and solvable automata. Theoret. Comput. Sci. 172, 273–279 (1997)MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Salomaa, A.: Composition sequences for functions over a finite domain. Theoret. Comput. Sci. 292, 263–281 (2003)MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Sandberg, S.: Homing and synchronizing sequences. In: Broy, M., Jonsson, B., Katoen, J.-P., Leucker, M., Pretschner, A. (eds.) Model-Based Testing of Reactive Systems. LNCS, vol. 3472, pp. 5–33. Springer, Heidelberg (2005)Google Scholar
  14. 14.
    Trahtman, A.N.: The Černý conjecture for aperiodic automata. Discrete Math. Theoret. Comp. Sci. 9(2), 3–10 (2007)MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Mikhail V. Volkov
    • 1
  1. 1.Department of Mathematics and Mechanics, Ural State University, 620083 EkaterinburgRussia

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