Dualizability of automatic algebras

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

On the dualisabilty of finite {0, 1 }-valued unary algebras with zero.

This thesis provides a few results regarding the natural dualisability of certain {0, 1}-valued unary algebras with zero. We use pp-formulae to develop a sufficient criterion for non-dualisability of such algebras. With this criterion, we show that {0, 1}-valued unary algebras with zero with unique rows whose rows form an order ideal (with respect to the lattice order {0, 1}ⁿ under 0 < 1) are not dualisable if its rows do not form an lattice order. For the case where the rows do form a lattice, we use the Interpolation Condition to show that the algebra is dualisable. The last result of this thesis provides another sufficient criterion for non-dualisability by looking at two-term reducts. --Leaf ii.The original print copy of this thesis may be available here: http://wizard.unbc.ca/record=b195332