Improving the Upper Bound on the Length of the Shortest Reset Word

@inproceedings{Szykula2018ImprovingTU,
  title={Improving the Upper Bound on the Length of the Shortest Reset Word},
  author={Marek Szykula},
  booktitle={STACS},
  year={2018}
}
We improve the best upper bound on the length of the shortest reset words of synchronizing automata. The new bound is (15617n 3 + 7500n 2 + 9375n − 31250)/93750. So far, the best general upper bound was (n 3 − n)/6 − 1 obtained by Pin and Frankl in 1983. Despite a number of efforts, the bound remained unchanged for about 34 years. The new upper bound improves the coefficient 1/6 at n 3 by 4/46875. A word is avoiding for a state q if after reading the word, the automaton cannot be in q. We prove… CONTINUE READING
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