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DOI: 10.4230/LIPIcs.MFCS.2019.29

The Quantifier Alternation Hierarchy of Synchronous Relations

Authors: Diego Figueira, Varun Ramanathan, and Pascal Weil

Published in: LIPIcs, Volume 138, 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)

Abstract

The class of synchronous relations, also known as automatic or regular, is one of the most studied subclasses of rational relations. It enjoys many desirable closure properties and is known to be logically characterized: the synchronous relations are exactly those that are defined by a first-order formula on the structure of all finite words, with the prefix, equal-length and last-letter predicates. Here, we study the quantifier alternation hierarchy of this logic. We show that it collapses at level Sigma_3 and that all levels below admit decidable characterizations. Our results reveal the connections between this hierarchy and the well-known hierarchy of first-order defined languages of finite words.

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Diego Figueira, Varun Ramanathan, and Pascal Weil. The Quantifier Alternation Hierarchy of Synchronous Relations. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 29:1-29:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{figueira_et_al:LIPIcs.MFCS.2019.29,
  author =	{Figueira, Diego and Ramanathan, Varun and Weil, Pascal},
  title =	{{The Quantifier Alternation Hierarchy of Synchronous Relations}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{29:1--29:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-117-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{138},
  editor =	{Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.29},
  URN =		{urn:nbn:de:0030-drops-109735},
  doi =		{10.4230/LIPIcs.MFCS.2019.29},
  annote =	{Keywords: synchronous relations, automatic relations, first-order logic, characterization, quantifier alternation}
}

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The Quantifier Alternation Hierarchy of Synchronous Relations

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