有序{ AND，OR }-分解与二元决策图
Ordered {AND, OR}-Decomposition and Binary-Decision Diagram
摘要：
在知识编译（KC）的背景下，我们研究了增加两种分解节点的有序二元决策图（OBDD）的效果，即，与-顶点和或-顶点，分别表示命题知识库的合取和析取分解。由此产生的知识编译语言被称为有序{AND，OR}-分解和二进制决策图（OAODD）。粗略地说，以前的几种语言可以被看作是特殊类型的OAODD，包括OBDD，与/或二元决策图（AOBDD），带有隐含文字的OBDD（OBDD-L），多级分解图（MLDD）。一方面，我们提出了一些家庭的算法，可以将一些片段的OAODD到其他人;另一方面，我们提出了一套丰富的多项式时间算法，执行逻辑运算。根据这些算法，以及理论分析，我们描述的空间效率和易处理的OAODD和它的一些片段相对于评价标准的KC地图。最后，给出了一个将负范式公式转换为OAODD的编译算法。
英文摘要：
In the context of knowledge compilation (KC), we study the effect of augmenting Ordered Binary Decision Diagrams (OBDD) with two kinds of decomposition nodes, i.e., AND-vertices and OR-vertices which denote conjunctive and disjunctive decomposition of propositional knowledge bases, respectively. The resulting knowledge compilation language is called Ordered {AND, OR}-decomposition and binary-Decision Diagram (OAODD). Roughly speaking, several previous languages can be seen as special types of OAODD, including OBDD, AND/OR Binary Decision Diagram (AOBDD), OBDD with implied Literals (OBDD-L), Multi-Level Decomposition Diagrams (MLDD). On the one hand, we propose some families of algorithms which can convert some fragments of OAODD into others; on the other hand, we present a rich set of polynomial-time algorithms that perform logical operations. According to these algorithms, as well as theoretical analysis, we characterize the space efficiency and tractability of OAODD and its some fragments with respect to the evaluating criteria in the KC map. Finally, we present a compilation algorithm which can convert formulas in negative normal form into OAODD.
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