Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH scholarly article en Lohrey, Markus; Zetzsche, Georg https://www.dagstuhl.de/lipics License: Creative Commons Attribution 3.0 Unported license (CC-BY 3.0)
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URN: urn:nbn:de:0030-drops-127364
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Knapsack and the Power Word Problem in Solvable Baumslag-Solitar Groups

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Abstract

We prove that the power word problem for the solvable Baumslag-Solitar groups BS(1,q) = ⟨ a,t ∣ t a t^{-1} = a^q ⟩ can be solved in TC⁰. In the power word problem, the input consists of group elements g₁, …, g_d and binary encoded integers n₁, …, n_d and it is asked whether g₁^{n₁} ⋯ g_d^{n_d} = 1 holds. Moreover, we prove that the knapsack problem for BS(1,q) is NP-complete. In the knapsack problem, the input consists of group elements g₁, …, g_d,h and it is asked whether the equation g₁^{x₁} ⋯ g_d^{x_d} = h has a solution in ℕ^d.

BibTeX - Entry

@InProceedings{lohrey_et_al:LIPIcs:2020:12736,
  author =	{Markus Lohrey and Georg Zetzsche},
  title =	{{Knapsack and the Power Word Problem in Solvable Baumslag-Solitar Groups}},
  booktitle =	{45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)},
  pages =	{67:1--67:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-159-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{170},
  editor =	{Javier Esparza and Daniel Kr{\'a}ľ},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12736},
  URN =		{urn:nbn:de:0030-drops-127364},
  doi =		{10.4230/LIPIcs.MFCS.2020.67},
  annote =	{Keywords: computational group theory, matrix problems, Baumslag-Solitar groups}
}

Keywords: computational group theory, matrix problems, Baumslag-Solitar groups
Seminar: 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)
Issue date: 2020
Date of publication: 18.08.2020


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