Year: 2026
Type: article
Abstract: We survey selected open problems in the theory of synchronizing automata, centered around the famous Černý conjecture.A deterministic finite automaton is called synchronizing if it admits a reset word whose action maps all states to a single state.The Černý conjecture states that every synchronizing automaton with n states possesses a reset word of length at most (n -1) 2 .We discuss avoiding words, compressing a state with another, synchronization of a (given or any) subset, complexity of deciding the synchronizability, average reset threshold, and linear-algebraic methods.Some new auxiliary results are also presented.
DOI: 10.4204/eptcs.451.3
Author: Marek Szykuła
Institution: University of Wrocław
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
Funder: Narodowym Centrum Nauki
OpenAlex ID: W7204113530
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