On the interplay between Babai and Cerny's conjectures

2017/04/13 by François Gonze, Gonze, François, Vladimir V. Gusev +7
Biochemistry, Genetics and Molecular Biology · Computer Science · #Algorithms and Data Compression #DNA and Biological Computing #FOS: Computer and information sciences #FOS: Mathematics #Formal Languages and Automata Theory (cs.FL) #Group Theory (math.GR) #semigroups and automata theory

paper · doi:10.48550/arxiv.1704.04047

openalex publication_date 2017/04/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Motivated by the Babai conjecture and the Cerny 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 \tfracn(n-1)2. In addition, we study diameters of the pair digraphs of permutation automata and construct n-state permutation automata with diameter \tfracn²4 + o(n²).

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