On the existence and design of the best stack filter based associative memory

The associative memory of a stack filter is defined as the set of root signals of that filter. In a class of stack filters in which each filter´s root set contains a desired set of patterns, those filters whose root sets have the smallest cardinality are said to be minimal among all filters in that class for that set of patterns. A partial ordering is defined on the set of stack filters via the set inclusion operation. Under this partial ordering, stack filters are found that are upper and lower bounds for the set of minimal stack filters that are furthest from the sets of decreasing and increasing stack filters. Knowledge of this configuration leads to an algorithm that can produce a near-minimal filter for any desired set of patterns. This method of constructing associative memories does not require the desired set of patterns to be independent, and it can construct a better filter