Improving the upper bound on the length of the shortest reset words

M Szykuła - arXiv preprint arXiv:1702.05455, 2017 - arxiv.org
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) …

Černý's conjecture and the road colouring problem

J Kari, MV Volkov - Handbook of automata theory, 2021 - ems.press
Let A be a complete deterministic finite automaton (DFA) with input alphabet A and state set
Q. We say that such an automaton is synchronising if there exists a word w 2 A such that …

Synchronization of finite automata

MV Volkov - 2022 - elar.urfu.ru
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 …

Primitive automata that are synchronizing

I Rystsov, M Szykuła - arXiv preprint arXiv:2307.01302, 2023 - arxiv.org
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 …

[PDF][PDF] The Černý Conjecture Holds with High Probability.

C Nicaud - J. Autom. Lang. Comb., 2019 - people.irisa.fr
An automaton is synchronizing when there is a word that brings every state into one and the
same state. Such a word is called a synchronizing word, and Černý conjectured in 1964 that …

Experiments with synchronizing automata

A Kisielewicz, J Kowalski, M Szykuła - International Conference on …, 2016 - Springer
We have improved an algorithm generating synchronizing automata with a large length of
the shortest reset words. This has been done by refining some known results concerning …

New characterizations of primitive permutation groups with applications to synchronizing automata

S Hoffmann - Information and Computation, 2023 - Elsevier
For a finite permutation group on n elements we show the following (and variants thereof)
equivalences:(1) the permutation group is primitive,(2) in the transformation monoid …

Fast synchronization of random automata

C Nicaud - arXiv preprint arXiv:1404.6962, 2014 - arxiv.org
A synchronizing word for an automaton is a word that brings that automaton into one and the
same state, regardless of the starting position. Cerny conjectured in 1964 that if a n-state …

A machine learning approach to synchronization of automata

I Podolak, A Roman, M Szykuła, B Zieliński - Expert Systems with …, 2018 - Elsevier
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 …

Sync-maximal permutation groups equal primitive permutation groups

S Hoffmann - Descriptional Complexity of Formal Systems: 23rd IFIP …, 2021 - Springer
The set of synchronizing words of a given n-state automaton forms a regular language
recognizable by an automaton with 2^ nn 2 nn states. The size of a recognizing automaton …