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Refutation of Aslam's Proof that NP = P (0904.3912v2)
Published 24 Apr 2009 in cs.CC
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.