论文标题

部分可观测时空混沌系统的无模型预测

Coding Guidelines and Undecidability

论文作者

Bagnara, Roberto, Bagnara, Abramo, Hill, Patricia M.

论文摘要

储层计算是预测湍流的有力工具,其简单的架构具有处理大型系统的计算效率。然而,其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间,然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用,该系统模拟了湍流的若干特征。我们表明,使用径向基函数作为非线性投影器,即使只有部分观测并且不知道控制方程,也能稳健地捕捉复杂的系统非线性。最后,我们表明,当测量稀疏、不完整且带有噪声,甚至控制方程变得不准确时,我们的网络仍然可以产生相当准确的预测,从而为实际湍流系统的无模型预测铺平了道路。

The C and C++ programming languages are widely used for the implementation of software in critical systems. They are complex languages with subtle features and peculiarities that might baffle even the more expert programmers. Hence, the general prescription of language subsetting, which occurs in most functional safety standards and amounts to only using a "safer" subset of the language, is particularly applicable to them. Coding guidelines are the preferred way of expressing language subsets. Some guidelines are formulated in terms of the programming language and its implementation only: in this case they are amenable to automatic checking. However, due to fundamental limitations of computing, some guidelines are undecidable, that is, they are based on program properties that no current and future algorithm can capture in all cases. The most mature and widespread coding standards, the MISRA ones, explicitly tag guidelines with undecidable or decidable. It turns out that this information is not of secondary nature and must be taken into account for a full understanding of what the guideline is asking for. As a matter of fact, undecidability is a common source of confusion affecting many users of coding standards and of the associated checking tools. In this paper, we recall the notions of decidability and undecidability in terms that are understandable to any C/C++ programmer. The paper includes a systematic study of all the undecidable MISRA C:2012 guidelines, discussing the reasons for the undecidability and its consequences. We pay particular attention to undecidable guidelines that have decidable approximations whose enforcement would not overly constrain the source code. We also discuss some coding guidelines for which compliance is hard, if not impossible, to prove, even beyond the issue of decidability.

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