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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.2020.117
URN: urn:nbn:de:0030-drops-125240
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12524/
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Cadilhac, Michaël ; Mazowiecki, Filip ; Paperman, Charles ; Pilipczuk, Michał ; Sénizergues, Géraud

On Polynomial Recursive Sequences

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LIPIcs-ICALP-2020-117.pdf (0.7 MB)

Abstract

We study the expressive power of polynomial recursive sequences, a nonlinear extension of the well-known class of linear recursive sequences. These sequences arise naturally in the study of nonlinear extensions of weighted automata, where (non)expressiveness results translate to class separations. A typical example of a polynomial recursive sequence is b_n = n!. Our main result is that the sequence u_n = nⁿ is not polynomial recursive.

BibTeX - Entry

@InProceedings{cadilhac_et_al:LIPIcs:2020:12524,
  author =	{Micha{\"e}l Cadilhac and Filip Mazowiecki and Charles Paperman and Michał Pilipczuk and G{\'e}raud S{\'e}nizergues},
  title =	{{On Polynomial Recursive Sequences}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{117:1--117:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Artur Czumaj and Anuj Dawar and Emanuela Merelli},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12524},
  URN =		{urn:nbn:de:0030-drops-125240},
  doi =		{10.4230/LIPIcs.ICALP.2020.117},
  annote =	{Keywords: recursive sequences, expressive power, weighted automata, higher-order pushdown automata}
}

Keywords: recursive sequences, expressive power, weighted automata, higher-order pushdown automata
Collection: 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)
Issue Date: 2020
Date of publication: 29.06.2020

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