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DOI: 10.4230/LIPIcs.STACS.2023.52

Reconstructing Words Using Queries on Subwords or Factors

Authors: Gwenaël Richomme and Matthieu Rosenfeld

Published in: LIPIcs, Volume 254, 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)

Abstract

We study word reconstruction problems. Improving a previous result by P. Fleischmann, M. Lejeune, F. Manea, D. Nowotka and M. Rigo, we prove that, for any unknown word w of length n over an alphabet of cardinality k, w can be reconstructed from the number of occurrences as subwords (or scattered factors) of O(k²√{nlog₂(n)}) words. Two previous upper bounds obtained by S. S. Skiena and G. Sundaram are also slightly improved: one when considering information on the existence of subwords instead of on the numbers of their occurrences, and, the other when considering information on the existence of factors.

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Gwenaël Richomme and Matthieu Rosenfeld. Reconstructing Words Using Queries on Subwords or Factors. In 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 254, pp. 52:1-52:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{richomme_et_al:LIPIcs.STACS.2023.52,
  author =	{Richomme, Gwena\"{e}l and Rosenfeld, Matthieu},
  title =	{{Reconstructing Words Using Queries on Subwords or Factors}},
  booktitle =	{40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)},
  pages =	{52:1--52:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-266-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{254},
  editor =	{Berenbrink, Petra and Bouyer, Patricia and Dawar, Anuj and Kant\'{e}, Mamadou Moustapha},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2023.52},
  URN =		{urn:nbn:de:0030-drops-177041},
  doi =		{10.4230/LIPIcs.STACS.2023.52},
  annote =	{Keywords: Word reconstruction, Subwords, Factors}
}

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DOI: 10.4230/LIPIcs.MFCS.2016.81

Every Binary Pattern of Length Greater Than 14 Is Abelian-2-Avoidable

Authors: Matthieu Rosenfeld

Published in: LIPIcs, Volume 58, 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)

Abstract

We show that every binary pattern of length greater than 14 is abelian-2-avoidable. The best known upper bound on the length of abelian-2-unavoidable binary pattern was 118, and the best known lower bound is 7. We designed an algorithm to decide, under some reasonable assumptions, if a morphic word avoids a pattern in the abelian sense. This algorithm is then used to show that some binary patterns are abelian-2-avoidable. We finally use this list of abelian-2-avoidable pattern to show our result. We also discuss the avoidability of binary patterns on 3 and 4 letters.

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Matthieu Rosenfeld. Every Binary Pattern of Length Greater Than 14 Is Abelian-2-Avoidable. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 81:1-81:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{rosenfeld:LIPIcs.MFCS.2016.81,
  author =	{Rosenfeld, Matthieu},
  title =	{{Every Binary Pattern of Length Greater Than 14 Is Abelian-2-Avoidable}},
  booktitle =	{41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
  pages =	{81:1--81:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-016-3},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{58},
  editor =	{Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.81},
  URN =		{urn:nbn:de:0030-drops-64892},
  doi =		{10.4230/LIPIcs.MFCS.2016.81},
  annote =	{Keywords: combinatorics on words, pattern avoidance, abelian repetitions}
}

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Documents authored by Rosenfeld, Matthieu

Reconstructing Words Using Queries on Subwords or Factors

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Every Binary Pattern of Length Greater Than 14 Is Abelian-2-Avoidable

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