  We establish new combinatorial transcendence criteria for continued fraction
expansions. Let $\alpha = [0; a_1, a_2,...]$ be an algebraic number of degree
at least three. One of our criteria implies that the sequence of partial
quotients $(a_{\ell})_{\ell \ge 1}$ of $\alpha$ cannot be generated by a finite
automaton, and that the complexity function of $(a_{\ell})_{\ell \ge 1}$ cannot
increase too slowly.
