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On the interplay between Babai and ?erny`s conjectures
时间  Datetime
2017-05-10 15:00 — 16:00 
地点  Venue
Middle Lecture Room
报告人  Speaker
Mikhail V. Volkov (Волков Михаил Владимирович)
单位  Affiliation
Ural Federal University
邀请人  Host
Yaokun Wu
报告摘要  Abstract

Motivated by the Babai conjecture and the ?erný 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+5 and can attain the value n(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).

This is joint work with François GonzeVladimir GusevBalázs Gerencsér and Raphaël M. Jungers.

http://math.sjtu.edu.cn/conference/Bannai/2017/talk.php?20170510B