Binary Decision Diagrams (BDDs) have been used to represent logic models in a variety of research contexts, such as software product lines, circuit testing, and plasma confinement, among others. Although BDDs have proven to be very useful, the main problem with this technique is that synthesizing BDDs can be a frustratingly slow or even unsuccessful process, due to its heuristic nature. We present an extension of propositional logic to tackle one recurring phenomenon in logic modeling, namely groups of variables related by an exclusive-or relationship, and also consider two other extensions: one in which at least n variables in a group are true and another one for in which at most n variables are true. We add XOR, atLeast-n and atMost-n primitives to logic formulas in order to reduce the size of the input and also present algorithms to efficiently incorporate these constructions into the building of BDDs. We prove, among other results, that the number of nodes created during the process for XOR groups is reduced from quadratic to linear for the affected clauses. the XOR primitive is tested against eight logical models, two from industry and six from Kconfig-based open-source projects. Results range from no negative effects in models without XOR relations to performance gains well into two orders of magnitude on models with an abundance of this kind of relationship.

中文翻译：

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使用扩展逻辑基元进行高效的BDD构建

二进制决策图（BDD）已用于表示各种研究环境中的逻辑模型，例如软件产品线，电路测试和等离子约束等。尽管已证明BDD非常有用，但是此技术的主要问题在于，由于BDD的启发式性质，其合成可能是令人沮丧的缓慢甚至失败的过程。我们提出了命题逻辑的扩展，以解决逻辑建模中的一个重复现象，即与异或关系相关的变量组，并且还考虑了其​​他两个扩展：一个扩展，其中一组中至少n个变量为真，而另一个其中最多n变量为真。我们将XOR，atLeast-n和atMost-n原语添加到逻辑公式中，以减小输入的大小，并且还提出了将这些构造有效地合并到BDD中的算法。我们证明，除其他结果外，对于受影响的子句，在XOR组处理过程中创建的节点数量从二次减少为线性。XOR原语针对八个逻辑模型进行了测试，其中两个来自行业，六个来自基于Kconfig的开源项目。结果的范围从没有XOR关系的模型中没有负面影响到性能提升，到具有大量这种关系的模型上的两个数量级。