Enhancements of the encoding strategy of a discrete bidirectional associative memory (BAM) reported by B. Kosko (1987) are presented. There are two major concepts in this work: multiple training, which can be guaranteed to achieve recall of a single trained pair under suitable initial conditions of data, and dummy augmentation, which can be guaranteed to achieve recall of all trained pairs if attaching dummy data to the training pairs is allowable. In representative computer simulations, multiple training has been shown to lead to an improvement over the original Kosko strategy for recall of multiple pairs as well. A sufficient condition for a correlation matrix to make the energies of the training pairs be local minima is discussed. The use of multiple training and dummy augmentation concepts are illustrated, and theorems underlying the results are presented.

A retiming algorithm is presented which includes the effects of variable register, clock distribution, and interconnect delays. These delay components are incorporated into the retiming process by assigning register electrical characteristics (REC's) to each edge in the graph representation of a synchronous circuit. A matrix, called the sequential adjacency matrix (SAM), is presented that contains all path delays. Timing constraints for each data path are derived from this matrix. Vertex lags are assigned ranges rather than single values as in existing retiming algorithms. The approach used in the proposed algorithm is to initialize these ranges with unbounded values and to continuously tighten these ranges using localized timing constraints until an optimal solution is obtained. A branch and bound method is offered for the general retiming problem where the REC values are arbitrary. Certain monotonicity constraints can be placed on the REC values to permit the use of standard linear programming methods, thereby requiring significantly less computational time. These conditions and the feasibility of their application to practical circuits are presented. The algorithm is demonstrated on modified benchmark circuits and both increased clock frequencies and the elimination of all race conditions are observed.

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Necessary and sufficient conditions are derived for the weights of a generalized correlation matrix of a bidirectional associative memory (BAM) which guarantee the recall of all training pairs. A linear programming/multiple training (LP/MT) method that determines weights which satisfy the conditions when a solution is feasible is presented. The sequential multiple training (SMT) method is shown to yield integers for the weights, which are multiplicities of the training pairs. Computer simulation results, including capacity comparisons of BAM, LP/MT BAM, and SMT BAM, are presented.

The minimal number of times for using a pair for training to guarantee recall of that pair among a set of training pairs is derived for a bidirectional associative memory.