A bound for the shortest reset words for semisimple synchronizing automata via the packing number

@article{Rodaro2017ABF,
  title={A bound for the shortest reset words for semisimple synchronizing automata via the packing number},
  author={Emanuele Rodaro},
  journal={ArXiv},
  year={2017},
  volume={abs/1711.00651}
}
We show that if a semisimple synchronizing automaton with $n$ states has a minimal reachable non-unary subset of cardinality $r\ge 2$, then there is a reset word of length at most $(n-1)D(2,r,n)$, where $D(2,r,n)$ is the $2$-packing number for families of $r$-subsets of $[1,n]$.