Associative positive Boolean functions and their maximum stacking vector representations

Stack filters are based on positive Boolean functions (PBFs) as their window operators which are usually represented by Boolean expressions and take a large number of minterms or maxterms to represent them on average. Thus, a good expression of these functions will make it easy to investigate the properties and behaviors of stack filters. In this paper, a class of positive Boolean functions called associative positive Boolean functions (APBFs) are proposed. They can be represented by the maximum stacking vector representation. The total memory space needed in this representation is only O(n). It satisfies the requirement of associative memory of neural networks and is more efficient to store in memory. The retrieval or filtering operation based on this new representation is very simple and easy to handle. Furthermore, some basic operations upon this new representation and the transformation algorithms between this new representation and others are proposed