Slowly Synchronizing Automata with Idempotent Letters of Low Rank

@article{Volkov2018SlowlySA,
  title={Slowly Synchronizing Automata with Idempotent Letters of Low Rank},
  author={Mikhail V. Volkov},
  journal={ArXiv},
  year={2018},
  volume={abs/1807.07048}
}
We use a semigroup-theoretic construction by Peter Higgins in order to produce, for each even $n$, an $n$-state and 3-letter synchronizing automaton with the following two features: 1) all its input letters act as idempotent selfmaps of rank at most $\dfrac{n}2$; 2) its reset threshold is asymptotically equal to $\dfrac{n^2}2$. 
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References

Publications referenced by this paper.
SHOWING 1-10 OF 35 REFERENCES

Lower Bounds for the Length of Reset Words in Eulerian Automata

  • Int. J. Found. Comput. Sci.
  • 2013
VIEW 6 EXCERPTS
HIGHLY INFLUENTIAL

Poznámka k homogénnym eksperimentom s konečnými automatmi

Jan Černý
  • Matematicko-fyzikalny Časopis Slovenskej Akadémie Vied,
  • 1964
VIEW 10 EXCERPTS
HIGHLY INFLUENTIAL

On the interplay between černý and babai’s conjectures

François Gonze, Vladimir V. Gusev, Balázs Gerencsér, Raphaël M. Jungers, Mikhail V. Volkov
  • Int. J. Found. Comput. Sci.,
  • 2019
VIEW 1 EXCERPT

Slowly synchronizing automata with idempotent letters of low rank

Mikhail V. Volkov
  • arXiv preprint,
  • 2018
VIEW 1 EXCERPT