2026-07-23T17:37:46Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:6577 2024-03-06T10:38:45Z ddc:004 open_access

The Height of Piecewise-Testable Languages with Applications in Logical Complexity Karandikar, Prateek Schnoebelen, Philippe Descriptive complexity 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 paper 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 FO^2(A^*, subword), 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Prateek Karandikar and Philippe Schnoebelen 2016 Is Part Of LIPIcs, Volume 62, 25th EACSL Annual Conference on Computer Science Logic (CSL 2016) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CSL.2016.37 urn:nbn:de:0030-drops-65776 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2016.37 eng https://creativecommons.org/licenses/by/3.0/legalcode