The classification and associative memory capability of stack filters

The notion of the on-set of a positive Boolean function is used to classify stack filters into three different types, called decreasing, increasing, and mixed. The associative memory capability of each of these three types of stack filters is then investigated. The associative memory of a stack filter is defined to be 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. Some learning schemes are proposed to find minimal decreasing and increasing stack filters. It is also shown that, for any specified set of patterns, there is always a mixed stack filter which is minimal when one considers all stack filters which preserve those patterns. In this sense, mixed stack filters are always at least as good as decreasing or increasing stack filters.<>