"... In PAGE 13: ...Following this idea let us consider the function dim(T k;3) for small values of k stored in Table1 . The entries of this table are equal to the corresponding lower bounds implied by counting arguments and they are supported by constructing embeddings with the help of a computer [2].... In PAGE 13: ... This would lead to the upper bound lim k!1 dim(T k;3) k lim i!1 n0 + 5i k0 + 3i = 5 3: (17) The simplest realization of this idea would be to embed T 3;3 into Q5 and apply the standard arguments above. However, Table1 shows that this is not possible, and we have to have more knowledge on the embedding of T k0;3 into Qn0. To reduce the number of vertices considered under this approach we use a stronger in- ductive hypothesis, extending the tree T k;3 up to the tree ^ T k.... ..."

"... In PAGE 2: ... Besides shifting (x 3) and/or complementing My it is necessary to generate f 2 x M and +4 x M. An extension of the Wallace (1964) technique is used for recoding the multiplier as shown in Table4 . The two non- trivial summands, 2 x M and 4 x M, are obtained at the start of the multiplication process by using both halves of the adder.... In PAGE 3: ... Note that C, = 2, because (Z,,,), = 2, causing G, to have a value of 2. From the pattern of the above equations for the Q,,, variables, which directly implement the selection procedure of Table4 for the m = 6 digit pair, it is clear that Q,,, is the only one that has a value of 2. It is set to 2 by the term (ZO,,),Cs.... In PAGE 3: ... It is set to 2 by the term (ZO,,),Cs. Since Q,,, = 2, tree inputs T6,i attain the values of the summand variables M3,i which is exactly the action called for by Table4 . It should be noted that when a negative summand is to be used, 3 apos;s-complement arithmetic is used, that is, the 2 apos;s-complement of the summand is introduced into the tree with a 1 to be added in the low-order position.... ..."

"... In PAGE 8: ... 3.3 An algorithm for the expansion of ternary functions into three- dimensional lattice circuits This Section introduces, as an example, an algorithm in Table3 for realizing ternary Shannon expansion of ternary functions in three-dimensional lattice circuits using the joining method that was proposed in Theorem 1. This algorithm is developed for the following convention: in the octant (sub- space) that corresponds to the positive x-axis, positive y-axis, and positive z-axis: (1) expand the nodes in-to-out and (2) join the cofactors counter clock wise (CCW).... ..."