Synchronizing automata of bounded rank

Authors:
Vladimir V. Gusev
Affiliations:
Institute of Mathematics and Computer Science, Ural Federal University, Ekaterinburg, Russia
Venue:
CIAA'12 Proceedings of the 17th international conference on Implementation and Application of Automata
Year:
2012

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Abstract

We reduce the problem of synchronization of an n-state automaton with letters of rank at most rn to the problem of synchronization of an r-state automaton with constraints given by a regular language. Using this technique we construct a series of synchronizing n-state automata in which every letter has rank rn and whose reset threshold is at least r2−r−1 Moreover, if $r \frac{n}{2}$, such automata are strongly connected.