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) …
synchronizing automata. The new bound is slightly better than $114 n^ 3/685+ O (n^ 2) …
Černý's conjecture and the road colouring problem
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 …
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 …
concerned with the case of complete deterministic automata. Algorithmic and complexity …
Primitive automata that are synchronizing
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 …
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 …
same state. Such a word is called a synchronizing word, and Černý conjectured in 1964 that …
Experiments with synchronizing automata
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 …
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 …
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 …
same state, regardless of the starting position. Cerny conjectured in 1964 that if a n-state …
A machine learning approach to synchronization of automata
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 …
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 …
recognizable by an automaton with 2^ nn 2 nn states. The size of a recognizing automaton …