Improved upper bounds on synchronizing nondeterministic automata

Authors:
Zsolt Gazdag;Szabolcs Iván;Judit Nagy-György
Affiliations:
Eötvös Loránd University, Budapest, Hungary;University of Szeged, Szeged, Hungary;University of Szeged, Szeged, Hungary
Venue:
Information Processing Letters
Year:
2009

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Abstract

We show that i-directable nondeterministic automata can be i-directed with a word of length O(2^n) for i=1,2, where n stands for the number of states. Since for i=1,2 there exist i-directable automata having i-directing words of length @W(2^n), these upper bounds are asymptotically optimal. We also show that a 3-directable nondeterministic automaton with n states can be 3-directed with a word of length O(n^2@?43^n), improving the previously known upper bound O(2^n). Here the best known lower bound is @W(33^n).