Primitive digraphs with large exponents and slowly synchronizing automata

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.

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

References in corpus (1)

• The Complexity of Finding Reset Words in Finite Automata

Cited by in corpus (6)

• Synchronizing Automata with Extremal Properties
• Experiments with Synchronizing Automata
• An Extremal Series of Eulerian Synchronizing Automata
• A bound for the shortest reset words for semisimple synchronizing automata via the packing number
• On the Number of Synchronizing Colorings of Digraphs
• On shortest products for nonnegative matrix mortality