Improving the upper bound the length of the shortest reset words

  title={Improving the upper bound the length of the shortest reset words},
  author={Marek Szykula},
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 114n3/685+O(n2). The Černý conjecture states that (n−1)2 is an upper bound. So far, the best general upper bound was (n3−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 reading the… CONTINUE READING


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