English

Complexity Classes and Theories for the Comparator Circuit Value Problem

Computational Complexity 2011-10-06 v2 Logic in Computer Science

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*.

Keywords

Cite

@article{arxiv.1106.4142,
  title  = {Complexity Classes and Theories for the Comparator Circuit Value Problem},
  author = {Stephen A. Cook and Dai Tri Man Le and Yuli Ye},
  journal= {arXiv preprint arXiv:1106.4142},
  year   = {2011}
}

Comments

This version was substantially rewritten, where several proofs were rewritten and many typos and mistakes were fixed. A shorter version of this paper appeared in CSL 2011

R2 v1 2026-06-21T18:25:22.074Z