A Note on a Recent Attempt to Improve the Pin-Frankl Bound
  We provide a counterexample to a lemma used in a recent tentative improvement of the the Pin-Frankl bound for synchronizing automata. This example naturally leads us to formulate an open question, whose answer could fix the line of proof, and improve the bound. 
Fran\c{c}ois Gonze, Rapha\"el M. Jungers, A. N. Trahtman
cs.FL