A note on a recent attempt to improve the Pin-Frankl bound

François Gonze (1) , Raphaël M. Jungers (1) , Avraham N. Trahtman (2)

1 ICTEAM - Institute of Information and Communication Technologies, Electronics and Applied Mathematics
2 Department of Mathematics [Ramat Gan]

We provide a counterexample to a lemma used in a recent tentative improvement of the Pin-Frankl bound for synchronizing automata. This example naturally leads us to formulate an open question, whose answer could fix the line of the proof, and improve the bound.

Mots clés: Automata; Synchronization; Cerny’s conjecture

Domaines: Mathématique discrète [cs.DM]

François Gonze, Raphaël M. Jungers, Avraham N. Trahtman. A note on a recent attempt to improve the Pin-Frankl bound. Discrete Mathematics and Theoretical Computer Science, 2015, Vol. 17 no. 1 (1), pp.307--308. ⟨10.46298/dmtcs.2101⟩. ⟨hal-01196844⟩