  The paper studies the main aspects of the realization of 2 x 2 ternary
reversible circuits based on cycles, considering the results of the realization
of all 362,880 2 x 2 ternary reversible functions. It has been shown that in
most cases, realizations obtained with the MMD+ algorithm have a lower
complexity (in terms of cost) than realizations based on cycles. In the paper
it is shown under which conditions realizations based on transpositions may
have a higher or a lower cost than realizations using larger cycles. Finally it
is shown that there are a few special cases where realizations based on
transpositions have the same cost or possibly lower cost than the MMD+ based
realizations. Aspects of scaleability are considered in terms of 2 x 2-based n
x n reversible circuits.
