Synchronizing groups and automata

@article{Arnold2006SynchronizingGA,
  title={Synchronizing groups and automata},
  author={Fredrick Arnold and Benjamin Steinberg},
  journal={Theor. Comput. Sci.},
  year={2006},
  volume={359},
  pages={101-110}
}
Pin showed that every p-state automaton (p a prime) containing a cyclic permutation and a non-permutation has a synchronizing word of length at most (p− 1). In this paper we consider permutation automata with the property that adding any non-permutation will lead to a synchronizing word and establish bounds on the lengths of such synchronizing words. In particular, we show that permutation groups whose permutation character over the rationals splits into a sum of only two irreducible characters… CONTINUE READING

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