On the Interplay Between Babai and Černý’s Conjectures

Gonze, François;Gusev, Vladimir;Gerencser, Balazs;Jungers, Raphaël;Volkov, Mikhail V.
(2017) 21st International Conference, DLT 2017 — Location: Liege, Belgium (7.August.2017)

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Authors
  • Gonze, FrançoisUCLouvain
    Author
  • Gusev, VladimirUCLouvain
    Author
  • Gerencser, BalazsUCLouvain
    Author
  • Jungers, RaphaëlUCLouvain
    Author
  • Volkov, Mikhail V.Ural Federal University
    Author
Abstract
Motivated by the Babai conjecture and the Černý conjecture, we study the reset thresholds of automata with the transition monoid equal to the full monoid of transformations of the state set. For automata with n states in this class, we prove that the reset thresholds are upper-bounded by 2n2−6n+52n2−6n+5 and can attain the value n(n−1)2n(n−1)2 . In addition, we study diameters of the pair digraphs of permutation automata and construct n-state permutation automata with diameter n24+o(n2)n24+o(n2) .
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Gonze, F., Gusev, V., Gerencser, B., Jungers, R., & Volkov, M. V. (2017). On the Interplay Between Babai and Černý’s Conjectures. Developments in Language Theory : Lecture Notes in Computer Science, p. 185-197. https://doi.org/10.1007/978-3-319-62809-7_13