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An Associative Representation of Stack Neural

Networks - Maximum Stacking Vector

Representation

**Pao-Ta Yu and Rong-Chung Chen**

National Chung Cheng University

Chiayi, Taiwan 62107, R.O.C.

Stack neural networks (*SNNs*) are based on positive Boolean functions (*PBFs*) as their nonlinear threshold operators, which are conventionally represented by positive Boolean expressions with a large number of minterms or maxterms in their representations on average. Therefore, a new representation to represent the *PBF* is needed such that the computational capability of stack neural networks can be improved based on this new representation or data structure.

In this paper, a fundamental class of *PBFs*, called *associative positive Boolean functions* (*APBFs*), is proposed as a basic set of *PBFs* such that we can represent *PBFs* via an appropriate combination from this basic set. This fundamental class is the largest subclass of *PBFs* which can be represented by the *maximum stacking vector representation*. This new representation only requires O(*n*) memory space to store its data structure, where *n* is the number of input Boolean variables. Therefore, this new representation provides an efficient approach to storing *PBFs* in an associative memory style. Furthermore, the retrieval operation of stack neural networks based on this new data structure is developed in a very simple and efficient manner. Finally, some significant operations generated from this new representation are proposed to extend the operating capability of *APBFs*.

Keywords: stack neural networks, positive Boolean function, threshold decompostion, stacking property, *MSV*, *APBF*, meet, join

Received July 28, 1995; revised May 10, 1996.

Communicated by Wen-Hsiang Tsai.
^{*}This work was partially supported by National Science Council of R.O.C. under grant NSC 881-0408-E-194-503.