论句子决策图的相对简洁性
On the Relative Succinctness of Sentential Decision Diagrams
摘要：
Darwiche在2011年提出的句子决策图（SDD）是一种很有前途的知识编译表示类型。表示类型的相对简洁性是这一领域的一个重要课题。本文的目的是确定哪类布尔函数可以用相对于函数定义的变量数而言尺寸较小的SDD表示，为此，研究了多项式尺寸下不同表示类型的布尔函数集合，并将SDD与Darwiche和Marquis的经典知识编译图中的表示类型进行了比较。有序二叉决策图（OBDD）是一种流行的布尔函数数据结构。SDD的定义比OBDD更一般，但直到最近，布尔函数才提出多项式SDD大小，但指数OBDD大小。这一结果在几个方面得到加强。的主要结果是一个准多项式模拟SDDs等效的明确的非确定性OBDDs，一个不确定性的变体，其中存在的每个满意的输入正好有一个接受计算。作为一个副作用，一个开放的问题，SDD和自由二元决策图（FBDDs），这是更一般的OBDDs之间的相对简洁的答案。
英文摘要：
Sentential decision diagrams (SDDs) introduced by Darwiche in 2011 are a promising representation type used in knowledge compilation. The relative succinctness of representation types is an important subject in this area. The aim of the paper is to identify which kind of Boolean functions can be represented by SDDs of small size with respect to the number of variables the functions are defined on. For this reason the sets of Boolean functions representable by different representation types in polynomial size are investigated and SDDs are compared with representation types from the classical knowledge compilation map of Darwiche and Marquis. Ordered binary decision diagrams (OBDDs) which are a popular data structure for Boolean functions are one of these representation types. SDDs are more general than OBDDs by definition but only recently, a Boolean function was presented with polynomial SDD size but exponential OBDD size. This result is strengthened in several ways. The main result is a quasipolynomial simulation of SDDs by equivalent unambiguous nondeterministic OBDDs, a nondeterministic variant where there exists exactly one accepting computation for each satisfying input. As a side effect an open problem about the relative succinctness between SDDs and free binary decision diagrams (FBDDs) which are more general than OBDDs is answered.
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