Reset threshold of Martyugin’s two‑letter Eulerian automata
Show that for odd n, the reset threshold of the two‑letter Eulerian synchronizing automata proposed by Pavel Martyugin equals (n^2−5)/2.
References
In the class of Eulerian automata with two letters, Pavel Martyugin (unpublished) proposed a series of n-state synchronizing automata (with n odd) conjectured to have a reset threshold of \frac{n2-5}2. The exhaustive search experiments in confirmed Martyugin's conjecture for n = 5, 7, 9, 11; moreover, for each of these values of n, Martyugin's automaton turned out to be the only one with reset threshold \frac{n2-5}2. However, in the general case the conjecture remains unproved and the greatest lower bound for the maximum reset threshold of Eulerian synchronizing automata with two letters and n states (with n odd) currently available in the literature is \frac{n2-3n+ 4}{2} from.