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Varieties of Data Languages

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Abstract

We establish an Eilenberg-type correspondence for data languages, i.e. languages over an infinite alphabet. More precisely, we prove that there is a bijective correspondence between varieties of languages recognized by orbit-finite nominal monoids and pseudovarieties of such monoids. This is the first result of this kind for data languages. Our approach makes use of nominal Stone duality and a recent category theoretic generalization of Birkhoff-type theorems that we instantiate here for the category of nominal sets. In addition, we prove an axiomatic characterization of weak pseudovarieties as those classes of orbit-finite monoids that can be specified by sequences of nominal equations, which provides a nominal version of a classical theorem of Eilenberg and Schützenberger.

BibTeX - Entry

@InProceedings{urbat_et_al:LIPIcs:2019:10706,
  author =	{Henning Urbat and Stefan Milius},
  title =	{{Varieties of Data Languages}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{130:1--130:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-109-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{132},
  editor =	{Christel Baier and Ioannis Chatzigiannakis and Paola Flocchini and Stefano Leonardi},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/10706},
  URN =		{urn:nbn:de:0030-drops-107063},
  doi =		{10.4230/LIPIcs.ICALP.2019.130},
  annote =	{Keywords: Nominal sets, Stone duality, Algebraic language theory, Data languages}
}

Keywords: Nominal sets, Stone duality, Algebraic language theory, Data languages
Seminar: 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)
Issue date: 2019
Date of publication: 2019


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