Qi-Chao Wang

The compress-with-another threshold of Szyku{\l}a's Figure 3 family

We give a self-contained pair-automaton proof of the exact compress-with-another threshold of the corrected Figure 3 family from a recent survey of open problems in synchronizing automata. For every $p \geq 3$, the automaton has $n = 3p$ states and $\mu(q_0) = 4p = 4n/3$. The word $(ba)^p(ab)^p$ attains this value. Two...