  We make a start on one of George McNulty's Dozen Easy Problems: "Which finite
automatic algebras are dualizable?" We give some necessary and some sufficient
conditions for dualizability. For example, we prove that a finite automatic
algebra is dualizable if its letters act as an abelian group of permutations on
its states. To illustrate the potential difficulty of the general problem, we
exhibit an infinite ascending chain $\mathbf A_1 \le \mathbf A_2 \le \mathbf
A_3 \le ...b$ of finite automatic algebras that are alternately dualizable and
non-dualizable.
