The height of piecewise-testable languages and the complexity of the logic of subwords

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 o...

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Published in:Logical methods in computer science Vol. 15, Issue 2; no. 2
Main Authors: Karandikar, Prateek, Schnoebelen, Philippe
Format: Journal Article
Language:English
Published: Logical Methods in Computer Science Association 01.04.2019
Logical Methods in Computer Science e.V
Subjects:
Computer Science
computer science - formal languages and automata theory
computer science - logic in computer science
f.3.1
f.4.1
f.4.3
F.4.3
Computer Science - Logic in Computer Science
Computer Science - Formal Languages and Automata Theory
F.3.1
F.4.1
ISSN:1860-5974, 1860-5974
Online Access:Get full text
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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 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
AbstractList 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
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.
Author Karandikar, Prateek
Schnoebelen, Philippe
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Computer Science - Formal Languages and Automata Theory
F.3.1
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Snippet 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...
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computer science - formal languages and automata theory
computer science - logic in computer science
f.3.1
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Title The height of piecewise-testable languages and the complexity of the logic of subwords
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