2 Search Results for "Wilke, Richard"


Document
On the Union Closed Fragment of Existential Second-Order Logic and Logics with Team Semantics

Authors: Matthias Hoelzel and Richard Wilke

Published in: LIPIcs, Volume 152, 28th EACSL Annual Conference on Computer Science Logic (CSL 2020)


Abstract
We present syntactic characterisations for the union closed fragments of existential second-order logic and of logics with team semantics. Since union closure is a semantical and undecidable property, the normal form we introduce enables the handling and provides a better understanding of this fragment. We also introduce inclusion-exclusion games that turn out to be precisely the corresponding model-checking games. These games are not only interesting in their own right, but they also are a key factor towards building a bridge between the semantic and syntactic fragments. On the level of logics with team semantics we additionally present restrictions of inclusion-exclusion logic to capture the union closed fragment. Moreover, we define a team based atom that when adding it to first-order logic also precisely captures the union closed fragment of existential second-order logic which answers an open question by Galliani and Hella.

Cite as

Matthias Hoelzel and Richard Wilke. On the Union Closed Fragment of Existential Second-Order Logic and Logics with Team Semantics. In 28th EACSL Annual Conference on Computer Science Logic (CSL 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 152, pp. 25:1-25:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


Copy BibTex To Clipboard

@InProceedings{hoelzel_et_al:LIPIcs.CSL.2020.25,
  author =	{Hoelzel, Matthias and Wilke, Richard},
  title =	{{On the Union Closed Fragment of Existential Second-Order Logic and Logics with Team Semantics}},
  booktitle =	{28th EACSL Annual Conference on Computer Science Logic (CSL 2020)},
  pages =	{25:1--25:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-132-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{152},
  editor =	{Fern\'{a}ndez, Maribel and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2020.25},
  URN =		{urn:nbn:de:0030-drops-116681},
  doi =		{10.4230/LIPIcs.CSL.2020.25},
  annote =	{Keywords: Higher order logic, Existential second-order logic, Team semantics, Closure properties, Union closure, Model-checking games, Syntactic charactisations of semantical fragments}
}
Document
Improved Spectral Sparsification and Numerical Algorithms for SDD Matrices

Authors: Ioannis Koutis, Alex Levin, and Richard Peng

Published in: LIPIcs, Volume 14, 29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012)


Abstract
We present three spectral sparsification algorithms that, on input a graph G with n vertices and m edges, return a graph H with n vertices and O(n log n/epsilon^2) edges that provides a strong approximation of G. Namely, for all vectors x and any epsilon>0, we have (1-epsilon) x^T L_G x <= x^T L_H x <= (1+epsilon) x^T L_G x, where L_G and L_H are the Laplacians of the two graphs. The first algorithm is a simple modification of the fastest known algorithm and runs in tilde{O}(m log^2 n) time, an O(log n) factor faster than before. The second algorithm runs in tilde{O}(m log n) time and generates a sparsifier with tilde{O}(n log^3 n) edges. The third algorithm applies to graphs where m>n log^5 n and runs in tilde{O}(m log_{m/ n log^5 n} n time. In the range where m>n^{1+r} for some constant r this becomes softO(m). The improved sparsification algorithms are employed to accelerate linear system solvers and algorithms for computing fundamental eigenvectors of dense SDD matrices.

Cite as

Ioannis Koutis, Alex Levin, and Richard Peng. Improved Spectral Sparsification and Numerical Algorithms for SDD Matrices. In 29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012). Leibniz International Proceedings in Informatics (LIPIcs), Volume 14, pp. 266-277, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)


Copy BibTex To Clipboard

@InProceedings{koutis_et_al:LIPIcs.STACS.2012.266,
  author =	{Koutis, Ioannis and Levin, Alex and Peng, Richard},
  title =	{{Improved Spectral Sparsification and Numerical Algorithms for SDD Matrices}},
  booktitle =	{29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012)},
  pages =	{266--277},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-35-4},
  ISSN =	{1868-8969},
  year =	{2012},
  volume =	{14},
  editor =	{D\"{u}rr, Christoph and Wilke, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2012.266},
  URN =		{urn:nbn:de:0030-drops-34348},
  doi =		{10.4230/LIPIcs.STACS.2012.266},
  annote =	{Keywords: Spectral sparsification, linear system solving}
}
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