Slowly synchronizing automata and digraphs

Authors:
Dmitry Ananichev;Vladimir Gusev;Mikhail Volkov
Affiliations:
Department of Mathematics and Mechanics, Ural State University, Ekaterinburg, Russia;Department of Mathematics and Mechanics, Ural State University, Ekaterinburg, Russia;Department of Mathematics and Mechanics, Ural State University, Ekaterinburg, Russia
Venue:
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Year:
2010

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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. These automata are closely related to primitive digraphs with large exponent.