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Improving the Upper Bound on the Length of the Shortest Reset Words
unpublished
We improve the best known upper bound on the length of the shortest reset words of synchronizing automata. The new bound is slightly better than 114n 3 /685+O(n 2). The Černý conjecture states that (n−1) 2 is an upper bound. So far, the best general upper bound was (n 3 −n)/6−1 obtained by J.-E. Pin and P. Frankl in 1982. Despite a number of efforts, it remained unchanged for about 35 years. To obtain the new upper bound we utilize avoiding words. A word is avoiding for a state q if after
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