Improving the upper bound the length of the shortest reset words

@article{Szykula2017ImprovingTU,
  title={Improving the upper bound the length of the shortest reset words},
  author={Marek Szykula},
  journal={ArXiv},
  year={2017},
  volume={abs/1702.05455}
}
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

References

Publications referenced by this paper.
SHOWING 1-10 OF 29 REFERENCES

Experiments with Synchronizing Automata

I. K. Rystsov, M. A. Spivak
  • Implementation and Application of Automata , volume 9705 of LNCS
  • 2016

Szykuła. Experiments with Synchronizing Automata

A. Kisielewicz, J. Kowalski
  • In Implementation and Application of Automata,
  • 2016

A Note on a Recent Attempt to Improve the Pin-Frankl Bound

F. Gonze, R. M Jungers, A. N. Trahtman
  • Discrete Mathematics and Theoretical Computer Science,
  • 2015