Refutation of Aslam's Proof that NP = P
Computational Complexity
2009-05-15 v2
Abstract
Aslam presents an algorithm he claims will count the number of perfect matchings in any incomplete bipartite graph with an algorithm in the function-computing version of NC, which is itself a subset of FP. Counting perfect matchings is known to be #P-complete; therefore if Aslam's algorithm is correct, then NP=P. However, we show that Aslam's algorithm does not correctly count the number of perfect matchings and offer an incomplete bipartite graph as a concrete counter-example.
Cite
@article{arxiv.0904.3912,
title = {Refutation of Aslam's Proof that NP = P},
author = {Frank Ferraro and Garrett Hall and Andrew Wood},
journal= {arXiv preprint arXiv:0904.3912},
year = {2009}
}
Comments
13 pages, 2 figures, a response to Aslam's paper (arXiv:0812.1385v11) and the underlying arguments (arXiv:0812.1385v9). Very minor content changes and typos fixed