一句话：系统研究分段可测试语言的高度，并据此证明子词序上的二变量一阶逻辑仅能表达分段可测试性质且具初等复杂度。
本文研究分段可测试语言（piecewise-testable languages）的高度：用排除和要求若干子词来定义语言 L 时所需词的最大长度。该高度是一种重要的描述复杂度度量，此前缺乏系统研究。文章发展了一系列新技术，用于界定有限语言以及由子词、超词闭包等相关运算所得语言的高度。作为应用，作者证明子词序下序列二变量一阶逻辑 FO^2(A*, ⊑) 只能表达分段可测试性质，并具有初等复杂度。本文是 CSL 2016 论文的完整版。
The height of a piecewise-testable language $L$ is the maximum length of the words needed to define $L$ by excluding and requiring given subwords. The height of $L$ is an important descriptive complexity measure that has not yet been investigated in a systematic way. This article develops a series of new techniques for bounding the height of finite languages and of languages obtained by taking closures by subwords, superwords and related operations. As an application of these results, we show that $\mathsf{FO}^2(A^*,\sqsubseteq)$, the two-variable fragment of the first-order logic of sequences with the subword ordering, can only express piecewise-testable properties and has elementary complexity. Comment: This article is a full version of "The height of piecewise-testable languages with applications in logical complexity", in Proc. CSL 2016, LIPiCS 62:37
@article{paperbot801,
title = {The height of piecewise-testable languages and the complexity of the logic of subwords},
author = {Prateek Karandikar and Philippe Schnoebelen},
journal = {Logical Methods in Computer Science},
volume = {Volume 15, Issue 2},
year = {2019},
doi = {10.23638/lmcs-15(2:6)2019}
}