## Karandikar, Prateek and Schnoebelen, Philippe - The height of piecewise-testable languages and the complexity of the logic of subwords

lmcs:4850 - Logical Methods in Computer Science, April 30, 2019, Volume 15, Issue 2
The height of piecewise-testable languages and the complexity of the logic of subwords

Authors: Karandikar, Prateek and Schnoebelen, Philippe

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.

Source : oai:arXiv.org:1511.01807
DOI : 10.23638/LMCS-15(2:6)2019
Volume: Volume 15, Issue 2
Published on: April 30, 2019
Submitted on: September 24, 2018
Keywords: Computer Science - Logic in Computer Science,Computer Science - Formal Languages and Automata Theory,F.4.1,F.4.3,F.3.1