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A formal theory for the complexity class associated with the stable marriage problem. (English) Zbl 1247.68095

Bezem, Marc (ed.), Computer science logic (CSL’11). 25th international workshop, 20th annual conference of the EACSL, Bergen, Norway, September 12–15, 2011. Wadern: Schloss Dagstuhl – Leibniz Zentrum für Informatik (ISBN 978-3-939897-32-3). LIPIcs – Leibniz International Proceedings in Informatics 12, 381-395, electronic only (2011).
Summary: 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*.
For the entire collection see [Zbl 1237.68014].

MSC:

68Q15 Complexity classes (hierarchies, relations among complexity classes, etc.)
03D15 Complexity of computation (including implicit computational complexity)
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