On smallest synchronizing terms over constant alphabets

We show a subexponential lower bound on the reset threshold of synchronizing deterministic finite tree automata (DTA) over alphabets of just two symbols. This significantly improves the previous one, which was quadratic in the number of states. Our result also narrows the gap towards the lower bound for DTA over alphabets that grow linearly with the number of states, as well as the best known upper bound, both of which are currently exponential.