Associative Positive Boolean Functions and Their Matrix

• Main Authors: Chen, Rong Chung, 陳榮昌
• Other Authors: Yu, Pao Ta
• Format: Others
• Language: en_US
• Published: 1993
• Online Access: http://ndltd.ncl.edu.tw/handle/79304982304879923949

碩士 === 國立中正大學 === 資訊工程研究所 === 81 === Stack filters are nonlinear filters which are based on the positive Boolean functions (PBF) as their window operators and nonlinear operators. Thus, a good data structure of these functions will make us easy to investigate their properties and behaviors. Matrix representation of a PBF is such a good data structure that leads us into a new approach of the study of stack filters and stack neural networks. The powerful ability of matrix computation would make it easu to study stack filters and stack neural networks and also the broad fields that use the PBFs. In this thesis, we propose a subclass of positive Boolean functions called associative positive Boolean functions (APBFs) which can be represented by the matrix form. A matrix of size (n+1)*(n+1) is used to represent an n-variable APBF. It is better than the Boolean expression whose storage is of exponential order. Moreover, it satisfies the requirement of associative memory of neural networks and is more efficient to store in memory. The algorithms to transfer between this data structure and the Boolean expression are prosed. Furthermore, we also prosed the retrieval method and some basic Boolean operations upon this new data structure. So, all the operations upon this data structure can be established and we can use the matrix representation of this sbclass of the positive Boolean functions to study stack filters and stack neural networks.