SYNCHRONIZING QUASI-EULERIAN AND QUASI-ONE-CLUSTER AUTOMATA

We describe a new version of the so-called extension method that was used to prove quadratic upper bounds on the minimum length of reset words for various important classes of synchronizing automata. Our approach is formulated in terms of Markov chains; it is in a sense dual to the usual extension method and improves on a recent result by Jungers. As an application, we obtain a quadratic upper bounds on the minimum length of reset words for generalizations of Eulerian and one-cluster automata. Finally, we show that the proposed approach is in some sense equivalent to the extension method.