# Combinatorics Seminar 2017

Date: Wed, May 10, 2017

Time: 15:00 - 16:00

Venue: Middle Meeting Room

Title: On the interplay between Babai and Černý's conjectures

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 $2n^2-6n+5$ 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 $\tfrac{n^2}{4} + o(n^2)$.

This is joint work with François Gonze, Vladimir Gusev, Balázs Gerencsér and Raphaël M. Jungers.

Slides: View slides

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