- 作者: 施兆翀
- 作者服務機構: 國立臺灣大學
- 中文摘要: 本論文討論一個能夠同時表達邏輯電路之輸出函數(Output function)及其線路結構(topological structure)的數學方法。此模型是根據那些線路內的途徑(networkpaths)間之「通用性」關係(compatibillity relationship)所構成。並可由此關係導出那些最大的通用性類(maximal compatibility classes)。這與Clegg所提倡的線路 SPOOF裹面的「類組」(products)成一對一的關係(isomorphism)。 對任何一個線路之通用性關係可以很容易就導出。同時,根據別人早已討論過的方伕,計算那些最大通用性類也是一件直接了當的事情。由於我們用來記錄(存放)那些通用性關係之資料結構(data structure)有成套(nest )之特性,故我們不單能更簡便的計算那些最大通用性類之外,同時當用計算機來作責料處理時,也能更充分去利用「套」的特性而節省可貴之記憶單位(memory space)。 在介紹完這個新的模型後,我們將介紹所用到的資料結構。並且將說明我們怎麼樣能夠利用這個新的數學模型來做更有效率的邏輯偵查(logic testing)。最後,我們並介紹怎樣決定一個一般的通用性關係是否可以由一個邏輯電路的途徑間之關係所導出。
- 英文摘要: A new and compact mathematical representation of both the topologicalstructure and the logic function of a circuit is discussed here. This newmodel is based on the compatibility relationship on the network paths whichis defined in such a way that the maximal compatibles are isomorphic tothe products in what Clegg has called the“SPOOF" for the network〔1,2, 3]. The determination of the compatibility relationships for a network isquite easy and it turns out that due to the work of others, finding all themaximal compatibles is also straightforward. Furthermore, the particularnested structure in which we record (store) the compatibility relations sim-plifies the task of determining the maximal compatibles [3].The nestedstructure is also beneficial in storage mangement when our representation isused in a computer program. After defining the new model, we describe the data structure that itleads to and show how it can be used for purposes of finding and evalua-ting test effectively. We also give necessary and sufficient conditions fora compatibility relationship to represent a loop-free logic network.
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