For the verification of systems using model-checking techniques, symbolic representations based on binary decision diagrams (BDDs) often help to tackle the well-known state-space explosion problem. Symbolic BDD-based representations have been also shown to be successful for the analysis of families of systems that arise, e.g., through configurable parameters or following the feature-oriented modeling approach. The state space of such system families face an additional exponential blowup in the number of parameters or features. It is well known that the order of variables in ordered BDDs is crucial for the size of the model representation. Especially for automatically generated models from real-world systems, family models might even be not constructible due to bad variable orders. In this paper we describe a technique, called iterative variable reordering, that can enable the construction of large-scale family models. We exemplify feasibility of our approach by means of an aircraft velocity control system with redundancy mechanisms modeled in the input language of the probabilistic model checker PRISM. We show that standard reordering and dynamic reordering techniques fail to construct the family model due to memory and time constraints, respectively, while the new iterative approach succeeds to generate a symbolic family model.

中文翻译：

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迭代变量重排序：驯服庞大的系统族

对于使用模型检查技术的系统验证，基于二元决策图 (BDD) 的符号表示通常有助于解决众所周知的状态空间爆炸问题。基于符号 BDD 的表示也已被证明可以成功地用于分析出现的系统族，例如，通过可配置参数或遵循面向特征的建模方法。这些系统族的状态空间在参数或特征的数量上面临额外的指数膨胀。众所周知，有序 BDD 中变量的顺序对于模型表示的大小至关重要。特别是对于从现实世界系统自动生成的模型，由于变量阶数不好，族模型甚至可能无法构建。在本文中，我们描述了一种技术，称为迭代变量重新排序，可以构建大规模的家庭模型。我们通过具有冗余机制的飞机速度控制系统来举例说明我们方法的可行性，该系统在概率模型检查器 PRISM 的输入语言中建模。我们表明，标准重新排序和动态重新排序技术分别由于内存和时间限制而无法构建族模型，而新的迭代方法成功生成了符号族模型。