Any Boolean function corresponds with a complete full binary decision tree. This tree can in turn be represented in a maximally compact form as a direct acyclic graph where common subtrees are factored and shared, keeping only one copy of each unique subtree. This yields the celebrated and widely used structure called reduced ordered binary decision diagram (ROBDD). We propose to revisit the classical compaction process to give a new way of enumerating ROBDDs of a given size without considering fully expanded trees and the compaction step. Our method also provides an unranking procedure for the set of ROBDDs. As a by-product we get a random uniform and exhaustive sampler for ROBDDs for a given number of variables and size.

中文翻译：

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二元决策图：从树压缩到采样

任何布尔函数都对应一个完整的二叉决策树。这棵树又可以以最大紧凑的形式表示为有向无环图，其中公共子树被分解和共享，每个唯一子树只保留一个副本。这产生了著名且广泛使用的结构，称为降序二元决策图 (ROBDD)。我们建议重新审视经典的压缩过程，以提供一种新的方法来枚举给定大小的 ROBDD，而无需考虑完全扩展的树和压缩步​​骤。我们的方法还为一组 ROBDD 提供了一个未排序的过程。作为副产品，对于给定数量的变量和大小，我们为 ROBDD 获得了一个随机统一且详尽的采样器。