Equation-based modelling is a powerful approach to tame the complexity of large-scale simulation problems. Equation-based tools automatically translate models into imperative languages. When confronted with nowadays’ problems, however, well assessed model translation techniques exhibit scalability issues that are particularly severe when models contain very large arrays. In fact, such models can be made very compact by enclosing equations into looping constructs, but reflecting the same compactness into the translated imperative code is nontrivial. In this paper, we face this issue by concentrating on a key step of equations-to-code translation, the equation/variable matching. We first show that an efficient translation of models with (large) arrays needs awareness of their presence, by defining a figure of merit to measure how much the looping constructs are preserved along the translation. We then show that the said figure of merit allows to define an optimal array-aware matching, and as our main result, that the so stated optimal array-aware matching problem is NP-complete. As an additional result, we propose a heuristic algorithm capable of performing array-aware matching in polynomial time. The proposed algorithm can be proficiently used by model translator developers in the implementation of efficient tools for large-scale system simulation.

基于方程的建模是解决大规模仿真问题复杂性的有效方法。基于方程的工具自动将模型翻译成命令式语言。然而，当面对当今的问题时，经过充分评估的模型转换技术表现出可扩展性问题，当模型包含非常大的数组时，这些问题尤其严重。事实上，通过将方程封装到循环结构中，可以使此类模型变得非常紧凑，但将相同的紧凑性反映到翻译的命令式代码中并非易事。在本文中，我们通过专注于方程到代码转换的关键步骤（方程/变量匹配）来面对这个问题。我们首先证明，具有（大）数组的模型的有效转换需要意识到它们的存在，通过定义一个品质因数来衡量在翻译过程中保留了多少循环结构。然后我们表明，所述品质因数允许定义最佳阵列感知匹配，并且作为我们的主要结果，所述最佳阵列感知匹配问题是 NP 完全的。作为额外的结果，我们提出了一种能够在多项式时间内执行数组感知匹配的启发式算法。模型转换器开发人员可以熟练地使用所提出的算法来实现大规模系统仿真的有效工具。我们提出了一种启发式算法，能够在多项式时间内执行数组感知匹配。模型转换器开发人员可以熟练地使用所提出的算法来实现大规模系统仿真的有效工具。我们提出了一种启发式算法，能够在多项式时间内执行数组感知匹配。模型转换器开发人员可以熟练地使用所提出的算法来实现大规模系统仿真的有效工具。