License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2019.125
URN: urn:nbn:de:0030-drops-107019
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/10701/
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Pin, Jean-Éric ; Reutenauer, Christophe

A Mahler's Theorem for Word Functions

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LIPIcs-ICALP-2019-125.pdf (0.5 MB)

Abstract

Let p be a prime number and let G_p be the variety of all languages recognised by a finite p-group. We give a construction process of all G_p-preserving functions from a free monoid to a free group. Our result follows from a new noncommutative generalization of Mahler's theorem on interpolation series, a celebrated result of p-adic analysis.

BibTeX - Entry

@InProceedings{pin_et_al:LIPIcs:2019:10701,
  author =	{Jean-{\'E}ric Pin and Christophe Reutenauer},
  title =	{{A Mahler's Theorem for Word Functions}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{125:1--125:13},
  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/2019/10701},
  URN =		{urn:nbn:de:0030-drops-107019},
  doi =		{10.4230/LIPIcs.ICALP.2019.125},
  annote =	{Keywords: group languages, interpolation series, pro-p metric, regularity preserving}
}

Keywords: group languages, interpolation series, pro-p metric, regularity preserving
Collection: 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)
Issue Date: 2019
Date of publication: 04.07.2019

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