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DOI: 10.4230/LIPIcs.CSL.2011.381
A Formal Theory for the Complexity Class Associated with the Stable Marriage Problem

Authors: Dai Tri Man Lê, Stephen A. Cook, and Yuli Ye

Published in: LIPIcs, Volume 12, Computer Science Logic (CSL'11) - 25th International Workshop/20th Annual Conference of the EACSL (2011)

Abstract
Subramanian defined the complexity class CC as the set of problems log-space reducible to the comparator circuit value problem. He proved that several other problems are complete for CC, including the stable marriage problem, and finding the lexicographical first maximal matching in a bipartite graph. We suggest alternative definitions of CC based on different reducibilities and introduce a two-sorted theory VCC* based on one of them. We sharpen and simplify Subramanian's completeness proofs for the above two problems and formalize them in VCC*.
Cite as

Dai Tri Man Lê, Stephen A. Cook, and Yuli Ye. A Formal Theory for the Complexity Class Associated with the Stable Marriage Problem. In Computer Science Logic (CSL'11) - 25th International Workshop/20th Annual Conference of the EACSL. Leibniz International Proceedings in Informatics (LIPIcs), Volume 12, pp. 381-395, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)

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@InProceedings{le_et_al:LIPIcs.CSL.2011.381,
  author =	{L\^{e}, Dai Tri Man and Cook, Stephen A. and Ye, Yuli},
  title =	{{A Formal Theory for the Complexity Class Associated with the Stable Marriage Problem}},
  booktitle =	{Computer Science Logic (CSL'11) - 25th International Workshop/20th Annual Conference of the EACSL},
  pages =	{381--395},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-32-3},
  ISSN =	{1868-8969},
  year =	{2011},
  volume =	{12},
  editor =	{Bezem, Marc},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2011.381},
  URN =		{urn:nbn:de:0030-drops-32440},
  doi =		{10.4230/LIPIcs.CSL.2011.381},
  annote =	{Keywords: bounded arithmetic, complexity theory, comparator circuits}
}
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