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Documents authored by Kaminski, Michael


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Sets of Linear Forms Which Are Hard to Compute

Authors: Michael Kaminski and Igor E. Shparlinski

Published in: LIPIcs, Volume 202, 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)


Abstract
We present a uniform description of sets of m linear forms in n variables over the field of rational numbers whose computation requires m(n - 1) additions. Our result is based on bounds on the height of the annihilating polynomials in the Perron theorem and an effective form of the Lindemann-Weierstrass theorem which is due to Sert (1999).

Cite as

Michael Kaminski and Igor E. Shparlinski. Sets of Linear Forms Which Are Hard to Compute. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 66:1-66:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{kaminski_et_al:LIPIcs.MFCS.2021.66,
  author =	{Kaminski, Michael and Shparlinski, Igor E.},
  title =	{{Sets of Linear Forms Which Are Hard to Compute}},
  booktitle =	{46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)},
  pages =	{66:1--66:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-201-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{202},
  editor =	{Bonchi, Filippo and Puglisi, Simon J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2021.66},
  URN =		{urn:nbn:de:0030-drops-145065},
  doi =		{10.4230/LIPIcs.MFCS.2021.66},
  annote =	{Keywords: Linear algorithms, additive complexity, effective Perron theorem, effective Lindemann-Weierstrass theorem}
}
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