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Documents authored by König, Daniel

Document
DOI: 10.4230/LIPIcs.STACS.2018.31
Automata Theory on Sliding Windows

Authors: Moses Ganardi, Danny Hucke, Daniel König, Markus Lohrey, and Konstantinos Mamouras

Published in: LIPIcs, Volume 96, 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)

Abstract
In a recent paper we analyzed the space complexity of streaming algorithms whose goal is to decide membership of a sliding window to a fixed language. For the class of regular languages we proved a space trichotomy theorem: for every regular language the optimal space bound is either constant, logarithmic or linear. In this paper we continue this line of research: We present natural characterizations for the constant and logarithmic space classes and establish tight relationships to the concept of language growth. We also analyze the space complexity with respect to automata size and prove almost matching lower and upper bounds. Finally, we consider the decision problem whether a language given by a DFA/NFA admits a sliding window algorithm using logarithmic/constant space.
Cite as

Moses Ganardi, Danny Hucke, Daniel König, Markus Lohrey, and Konstantinos Mamouras. Automata Theory on Sliding Windows. In 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 96, pp. 31:1-31:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{ganardi_et_al:LIPIcs.STACS.2018.31,
  author =	{Ganardi, Moses and Hucke, Danny and K\"{o}nig, Daniel and Lohrey, Markus and Mamouras, Konstantinos},
  title =	{{Automata Theory on Sliding Windows}},
  booktitle =	{35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)},
  pages =	{31:1--31:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-062-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{96},
  editor =	{Niedermeier, Rolf and Vall\'{e}e, Brigitte},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2018.31},
  URN =		{urn:nbn:de:0030-drops-84851},
  doi =		{10.4230/LIPIcs.STACS.2018.31},
  annote =	{Keywords: regular languages, sliding window algorithms}
}
Document
DOI: 10.4230/LIPIcs.STACS.2018.32
Knapsack Problems for Wreath Products

Authors: Moses Ganardi, Daniel König, Markus Lohrey, and Georg Zetzsche

Published in: LIPIcs, Volume 96, 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)

Abstract
In recent years, knapsack problems for (in general non-commutative) groups have attracted attention. In this paper, the knapsack problem for wreath products is studied. It turns out that decidability of knapsack is not preserved under wreath product. On the other hand, the class of knapsack-semilinear groups, where solutions sets of knapsack equations are effectively semilinear, is closed under wreath product. As a consequence, we obtain the decidability of knapsack for free solvable groups. Finally, it is shown that for every non-trivial abelian group G, knapsack (as well as the related subset sum problem) for the wreath product G \wr Z is NP-complete.
Cite as

Moses Ganardi, Daniel König, Markus Lohrey, and Georg Zetzsche. Knapsack Problems for Wreath Products. In 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 96, pp. 32:1-32:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{ganardi_et_al:LIPIcs.STACS.2018.32,
  author =	{Ganardi, Moses and K\"{o}nig, Daniel and Lohrey, Markus and Zetzsche, Georg},
  title =	{{Knapsack Problems for Wreath Products}},
  booktitle =	{35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)},
  pages =	{32:1--32:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-062-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{96},
  editor =	{Niedermeier, Rolf and Vall\'{e}e, Brigitte},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2018.32},
  URN =		{urn:nbn:de:0030-drops-85201},
  doi =		{10.4230/LIPIcs.STACS.2018.32},
  annote =	{Keywords: knapsack, wreath products, decision problems in group theory}
}
Document
DOI: 10.4230/LIPIcs.STACS.2017.35
Circuit Evaluation for Finite Semirings

Authors: Moses Ganardi, Danny Hucke, Daniel König, and Markus Lohrey

Published in: LIPIcs, Volume 66, 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)

Abstract
The circuit evaluation problem for finite semirings is considered, where semirings are not assumed to have an additive or multiplicative identity. The following dichotomy is shown: If a finite semiring R (i) has a solvable multiplicative semigroup and (ii) does not contain a subsemiring with an additive identity 0 and a multiplicative identity 1 != 0, then its circuit evaluation problem is in the complexity class DET (which is contained in NC^2). In all other cases, the circuit evaluation problem is P-complete.
Cite as

Moses Ganardi, Danny Hucke, Daniel König, and Markus Lohrey. Circuit Evaluation for Finite Semirings. In 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 66, pp. 35:1-35:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{ganardi_et_al:LIPIcs.STACS.2017.35,
  author =	{Ganardi, Moses and Hucke, Danny and K\"{o}nig, Daniel and Lohrey, Markus},
  title =	{{Circuit Evaluation for Finite Semirings}},
  booktitle =	{34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)},
  pages =	{35:1--35:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-028-6},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{66},
  editor =	{Vollmer, Heribert and Vall\'{e}e, Brigitte},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2017.35},
  URN =		{urn:nbn:de:0030-drops-69978},
  doi =		{10.4230/LIPIcs.STACS.2017.35},
  annote =	{Keywords: circuit value problem, finite semirings, circuit complexity}
}
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