Primitive digraphs with large exponents and slowly synchronizing automata
Formal Languages and Automata Theory
2014-11-25 v2
Abstract
We present several infinite series of synchronizing automata for which the minimum length of reset words is close to the square of the number of states. All these automata are tightly related to primitive digraphs with large exponent.
Keywords
Cite
@article{arxiv.1302.5793,
title = {Primitive digraphs with large exponents and slowly synchronizing automata},
author = {Dmitry S. Ananichev and Vladimir V. Gusev and Mikhail V. Volkov},
journal= {arXiv preprint arXiv:1302.5793},
year = {2014}
}
Comments
23 pages, 11 figures, 3 tables. This is a translation (with a slightly updated bibliography) of the authors' paper published in Russian in: Zapiski Nauchnyh Seminarov POMI [Kombinatorika i Teorija Grafov. IV], Vol. 402, 9-39 (2012), see ftp://ftp.pdmi.ras.ru/pub/publicat/znsl/v402/p009.pdf Version 2: a few typos are corrected