Structured d-DNNFs and SDDs are restricted negation normal form circuits used in knowledge compilation as target languages into which propositional theories are compiled. Structuredness is imposed by so-called vtrees. By definition SDDs are restricted structured d-DNNFs. Beame and Liew (2015) as well as Bova and Szeider (2017) mentioned the question whether structured d-DNNFs are really more general than SDDs w.r.t. polynomial-size representations (w.r.t. the number of Boolean variables the represented functions are defined on.) The main result in the paper is the proof that a function can be represented by SDDs of polynomial size if the function and its complement have polynomial-size structured d-DNNFs that respect the same vtree.

结构化的d- DNNF和SDD是受限的否定范式电路，用于知识汇编中，作为命题理论被编译成的目标语言。结构性是由所谓的vtree强加的。根据定义，SDD是受限制的结构化d -DNNF。Beame和Liew（2015）以及Bova和Szeider（2017）提出了以下问题：结构化d -DNNF是否真的比多项式大小表示形式的SDD更通用（写了表示函数所定义的布尔变量的数量。）本文的主要结果是证明，如果函数及其补码具有多项式大小的结构化d -DNNF且它们尊重同一vtree ，则该函数可以用多项式大小的SDD表示。