An Ashenhurst disjoint and non-disjoint decomposition of logic functions in Reed-Muller spectral domain
An Ashenhurst disjoint and non-disjoint decomposition of logic functions in Reed-Muller spectral domain
复制标题
DOI：
--
复制
发表时间：
2010-06
期刊：
影响因子：
--
通讯作者：
E. Hrynkiewicz;S. Kolodzinski
中科院分区：
文献类型：
--
作者：
E. Hrynkiewicz;S. Kolodzinski
本文探讨了里德 - 穆勒（Reed - Muller）谱域中逻辑函数分解的问题。针对基于查找表（LUT）的现场可编程门阵列（FPGA）中逻辑函数的实现，考虑了阿什赫斯特（Ashenhurst）分解。这些分解是在被分解函数的正极化里德 - 穆勒谱上进行的。文中阐述了在逻辑函数不相交和相交分解过程中，输入变量分配到自由集、有界集和公共集的问题。一种寻找有利公共变量集（从相交分解的角度）的方法是基于逻辑微分学的应用以及作者的经验。分解在里德 - 穆勒谱域中进行，是因为从作为里德 - 穆勒逆变换得到的逻辑函数的里德 - 穆勒形式中，布尔微分很容易计算。
The paper deals with the problems of logic function decomposition in Reed-Muller spectral domain. The Ashenhurst decompositions are considered with respect to implementation of logic functions in LUT based FPGA. The decompositions are executed on Positive Polarization Reed-Muller spectrum of decomposed functions. The problems of input variables assigning to the free set, bounded set and common set during logic function disjoint and non-disjoint decomposition were addressed. A method of finding profitable common variables set (from the point of view of non-disjoint decomposition) is based on utilisation of Logic Differential Calculus and authors experiences. The decomposition is carried out in Reed-Muller spectral domain because the Boolean differentials are easy calculated from Reed-Muller form of logic function which is obtained as reverse Reed-Muller transform.