On the Interplay Between Babai and Černý’s Conjectures

  • François Gonze
  • Vladimir V. Gusev
  • Balázs Gerencsér
  • Raphaël M. Jungers
  • Mikhail V. Volkov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10396)


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 \(2n^2-6n+5\) and can attain the value \(\tfrac{n(n-1)}{2}\). In addition, we study diameters of the pair digraphs of permutation automata and construct n-state permutation automata with diameter \(\tfrac{n^2}{4} + o(n^2)\).


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • François Gonze
    • 1
  • Vladimir V. Gusev
    • 1
    • 2
  • Balázs Gerencsér
    • 3
  • Raphaël M. Jungers
    • 1
  • Mikhail V. Volkov
    • 2
  1. 1.ICTEAM InstituteUniversité catholique de LouvainLouvain-la-NeuveBelgium
  2. 2.Ural Federal UniversityEkaterinburgRussia
  3. 3.Alfréd Rényi Institute of MathematicsBudapestHungary

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