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The Height of Piecewise-Testable Languages with Applications in Logical Complexity

Authors Prateek Karandikar, Philippe Schnoebelen

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Prateek Karandikar
Philippe Schnoebelen

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Prateek Karandikar and Philippe Schnoebelen. The Height of Piecewise-Testable Languages with Applications in Logical Complexity. In 25th EACSL Annual Conference on Computer Science Logic (CSL 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 62, pp. 37:1-37:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016) https://doi.org/10.4230/LIPIcs.CSL.2016.37

Abstract

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.

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  • Descriptive complexity

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