We investigate conjunctive normal form (CNF) encodings of a function represented with a decomposable negation normal form (DNNF). Several encodings of DNNFs and decision diagrams were considered by (Abío et al., 2016). The authors differentiate between encodings which implement consistency or domain consistency by unit propagation from encodings which are unit refutation complete or propagation complete. The difference is that in the former case we do not care about propagation strength of the encoding with respect to the auxiliary variables while in the latter case we treat all variables (the main and the auxiliary ones) in the same way. The currently known encodings of DNNF theories implement domain consistency. Building on these encodings we generalize the result of (Abío et al., 2016) on a propagation complete encoding of decision diagrams and present a propagation complete encoding of a DNNF and its generalization for variables with finite domains.

我们研究用可分解否定范式（DNNF）表示的函数的合取范式（CNF）编码。 (Abío et al., 2016) 考虑了 DNNF 和决策图的几种编码。作者区分了通过单元传播实现一致性或域一致性的编码与单元反驳完全或传播完全的编码。不同之处在于，在前一种情况下，我们不关心编码相对于辅助变量的传播强度，而在后一种情况下，我们以相同的方式处理所有变量（主变量和辅助变量）。当前已知的 DNNF 理论编码实现了域一致性。在这些编码的基础上，我们将（Abío et al., 2016）的结果推广到决策图的传播完整编码上，并提出了 DNNF 的传播完整编码及其对有限域变量的泛化。