Search Results

Documents authored by Krenn, Daniel

Artifact
Software
DOI: 10.4230/artifacts.22448
Fluctuation Find Min and Max

Authors: Clemens Heuberger, Daniel Krenn, and Tobias Lechner

Abstract
Cite as

Clemens Heuberger, Daniel Krenn, Tobias Lechner. Fluctuation Find Min and Max (Software, Code for Example 9). Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@misc{dagstuhl-artifact-22448,
   title = {{Fluctuation Find Min and Max}}, 
   author = {Heuberger, Clemens and Krenn, Daniel and Lechner, Tobias},
   note = {Software, version 1.0., Austrian Science Fund (FWF) [10.55776/DOC78], swhId: \href{https://archive.softwareheritage.org/swh:1:dir:e3d6789813ee435280117108c7bfd47809aeecc9;origin=https://gitlab.com/cheuberg/fluctuation-find-min-max;visit=swh:1:snp:4c5976f8bc6f69a47e4c593ebe5bee8e221afda3;anchor=swh:1:rev:eff7aab95599c61ea5c9102aceedfa8736742e3b}{\texttt{swh:1:dir:e3d6789813ee435280117108c7bfd47809aeecc9}} (visited on 2024-11-28)},
   url = {https://gitlab.com/cheuberg/fluctuation-find-min-max},
   doi = {10.4230/artifacts.22448},
}
Document
DOI: 10.4230/LIPIcs.AofA.2024.24
Analysis of Regular Sequences: Summatory Functions and Divide-And-Conquer Recurrences

Authors: Clemens Heuberger, Daniel Krenn, and Tobias Lechner

Published in: LIPIcs, Volume 302, 35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024)

Abstract
In the asymptotic analysis of regular sequences as defined by Allouche and Shallit, it is usually advisable to study their summatory function because the original sequence has a too fluctuating behaviour. It might be that the process of taking the summatory function has to be repeated if the sequence is fluctuating too much. In this paper we show that for all regular sequences except for some degenerate cases, repeating this process finitely many times leads to a "nice" asymptotic expansion containing periodic fluctuations whose Fourier coefficients can be computed using the results on the asymptotics of the summatory function of regular sequences by the first two authors of this paper. In a recent paper, Hwang, Janson, and Tsai perform a thorough investigation of divide-and-conquer recurrences. These can be seen as 2-regular sequences. By considering them as the summatory function of their forward difference, the results on the asymptotics of the summatory function of regular sequences become applicable. We thoroughly investigate the case of a polynomial toll function.
Cite as

Clemens Heuberger, Daniel Krenn, and Tobias Lechner. Analysis of Regular Sequences: Summatory Functions and Divide-And-Conquer Recurrences. In 35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 302, pp. 24:1-24:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{heuberger_et_al:LIPIcs.AofA.2024.24,
  author =	{Heuberger, Clemens and Krenn, Daniel and Lechner, Tobias},
  title =	{{Analysis of Regular Sequences: Summatory Functions and Divide-And-Conquer Recurrences}},
  booktitle =	{35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024)},
  pages =	{24:1--24:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-329-4},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{302},
  editor =	{Mailler, C\'{e}cile and Wild, Sebastian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AofA.2024.24},
  URN =		{urn:nbn:de:0030-drops-204597},
  doi =		{10.4230/LIPIcs.AofA.2024.24},
  annote =	{Keywords: Regular sequence, Divide-and-Conquer Recurrence, Summatory Function, Asymptotic Analysis}
}
Document
DOI: 10.4230/LIPIcs.AofA.2018.27
Analysis of Summatory Functions of Regular Sequences: Transducer and Pascal's Rhombus

Authors: Clemens Heuberger, Daniel Krenn, and Helmut Prodinger

Published in: LIPIcs, Volume 110, 29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018)

Abstract
The summatory function of a q-regular sequence in the sense of Allouche and Shallit is analysed asymptotically. The result is a sum of periodic fluctuations multiplied by a scaling factor. Each summand corresponds to an eigenvalues of absolute value larger than the joint spectral radius of the matrices of a linear representation of the sequence. The Fourier coefficients of the fluctuations are expressed in terms of residues of the corresponding Dirichlet generating function. A known pseudo Tauberian argument is extended in order to overcome convergence problems in Mellin-Perron summation. Two examples are discussed in more detail: The case of sequences defined as the sum of outputs written by a transducer when reading a q-ary expansion of the input and the number of odd entries in the rows of Pascal's rhombus.
Cite as

Clemens Heuberger, Daniel Krenn, and Helmut Prodinger. Analysis of Summatory Functions of Regular Sequences: Transducer and Pascal's Rhombus. In 29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 110, pp. 27:1-27:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

Copy BibTex To Clipboard

@InProceedings{heuberger_et_al:LIPIcs.AofA.2018.27,
  author =	{Heuberger, Clemens and Krenn, Daniel and Prodinger, Helmut},
  title =	{{Analysis of Summatory Functions of Regular Sequences: Transducer and Pascal's Rhombus}},
  booktitle =	{29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018)},
  pages =	{27:1--27:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-078-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{110},
  editor =	{Fill, James Allen and Ward, Mark Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AofA.2018.27},
  URN =		{urn:nbn:de:0030-drops-89204},
  doi =		{10.4230/LIPIcs.AofA.2018.27},
  annote =	{Keywords: Regular sequence, Mellin-Perron summation, summatory function, transducer, Pascal's rhombus}
}
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact