Several papers (e.g. [7, 23, 42]) have recently sought to give general frameworks for online structures and algorithms ([4]), and seeking to connect, if only by analogy, online and computable structure theory. These initiatives build on earlier work on online colouring and other combinatorial algorithms by Bean [10], Kierstead, Trotter et al. [48, 54, 57] and others, as we discuss below. In this paper we will look at such frameworks and illustrate them with examples from the first author’s MSc Thesis ([58]). In this thesis, Askes looks at online, adversarial online and strongly online algorithms and structures. Additionally, we prove some new theorems about online algorithms on graphs of bounded pathwidth as well as some new results on punctually 1-decidable structures.

中文翻译：

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在线、可计算和准时结构理论

最近有几篇论文（例如 [7, 23, 42]）试图为在线结构和算法（[4]）提供一般框架，并试图通过类比将在线和可计算结构理论联系起来。这些举措建立在 Bean [10]、Kierstead、Trotter 等人早期关于在线着色和其他组合算法的工作之上。[48, 54, 57] 和其他人，我们将在下面讨论。在本文中，我们将研究这些框架，并用第一作者的硕士论文（[58]）中的例子来说明它们。在这篇论文中，Askes 着眼于在线、对抗在线和强在线算法和结构。此外，我们在有界路径宽度图上证明了一些关于在线算法的新定理，以及关于准时 1 可判定结构的一些新结果。