We improve the best known upper bound on the length of the shortest reset words of
synchronizing automata. The new bound is slightly better than $114 n^ 3/685+ O (n^ 2) …

We refine a uniform algebraic approach for deriving upper bounds on reset thresholds of
synchronizing automata. We express the condition that an automaton is synchronizing in …

A survey of the state-of-the-art of the theory of synchronizing automata is given in its part
concerned with the case of complete deterministic automata. Algorithmic and complexity …

A deterministic finite (semi) automaton is primitive if its transition monoid (semigroup) acting
on the set of states has no non-trivial congruences. It is synchronizing if it contains a …

It was conjectured by Černý in 1964, that a synchronizing DFA on n states always has a
synchronizing word of length at most (n− 1) 2, and he gave a sequence of DFAs for which …

We present a novel method to predict the length of the shortest synchronizing words of a
finite automaton by applying the machine learning approach. We introduce several so-called …

Synchronizing sequences for large-scale automata have gained popularity recently due to
their practical use cases especially to have a faster and better testing process. In many …

An automaton is synchronizing if there exists a word that sends all states of the automaton to
a single state. The reset threshold is the length of the shortest such word. We study the set …

Modern distributed information systems (DIS), based on the complex application of many
technologies, increasingly acquire the properties of multi-agent systems (MAS). Autonomy …

We present an infinite series of n-state Eulerian automata whose reset words have length at
least (n^ 2-3)/2. This improves the current lower bound on the length of shortest reset words …