This paper presents a new compressed representation of Boolean functions, called CFLOBDDs (for Context-Free-Language Ordered Binary Decision Diagrams). They are essentially a plug-compatible alternative to BDDs (Binary Decision Diagrams), and hence useful for representing certain classes of functions, matrices, graphs, relations, etc. in a highly compressed fashion. CFLOBDDs share many of the good properties of BDDs, but--in the best case--the CFLOBDD for a Boolean function can be exponentially smaller than any BDD for that function. Compared with the size of the decision tree for a function, a CFLOBDD--again, in the best case--can give a double-exponential reduction in size. They have the potential to permit applications to (i) execute much faster, and (ii) handle much larger problem instances than has been possible heretofore. CFLOBDDs are a new kind of decision diagram that go beyond BDDs (and their many relatives). The key insight is a new way to reuse sub-decision-diagrams: components of CFLOBDDs are structured hierarchically, so that sub-decision-diagrams can be treated as standalone ''procedures'' and reused. We applied CFLOBDDs to the problem of simulating quantum circuits, and found that for several standard problems the improvement in scalability--compared to simulation using BDDs--is quite dramatic. In particular, the number of qubits that could be handled using CFLOBDDs was larger, compared to BDDs, by a factor of 128x for GHZ; 1,024x for BV; 8,192x for DJ; and 128x for Grover's algorithm. (With a 15-minute timeout, the number of qubits that CFLOBDDs can handle are 65,536 for GHZ, 524,288 for BV; 4,194,304 for DJ; and 4,096 for Grover's Algorithm.)

翻译：本文提出了一种新的布尔函数压缩表示方法，称为CFLOBDDs（上下文无关语言有序二叉决策图）。它们本质上是BDDs（二叉决策图）的即插即用替代方案，因此可用于以高度压缩的方式表示某些类别的函数、矩阵、图、关系等。CFLOBDDs继承了BDDs的许多优良特性，但在最佳情况下，布尔函数的CFLOBDD规模可比该函数的任何BDD呈指数级缩小。与函数的决策树规模相比，CFLOBDD在最佳情况下可实现规模的二次指数级缩减。它们具有让应用（i）运行速度显著提升，（ii）处理远超以往规模的实例的潜力。CFLOBDDs是一种全新的决策图，超越了BDDs（及其众多变体）。核心创新在于子决策图重用方式：CFLOBDD的组件采用分层结构，使得子决策图可作为独立的“过程”被重用。我们将CFLOBDDs应用于量子电路模拟问题，发现对于多个标准问题，相较于使用BDDs的模拟，其可扩展性的提升极为显著。具体而言，相较于BDDs，使用CFLOBDDs可处理的量子比特数在GHZ态上提升128倍；在BV算法上提升1,024倍；在DJ算法上提升8,192倍；在Grover算法上提升128倍。（在15分钟超时限制下，CFLOBDDs可处理的量子比特数分别为：GHZ态65,536个，BV算法524,288个，DJ算法4,194,304个，Grover算法4,096个。）