Data Structures and Algorithms


An Interesting Perspective to the P Versus NP Problem

Authors: Wenming Zhang

We discuss the P versus NP problem from the perspective of addition operation about polynomial functions. Two contradictory propositions for the addition operation are presented. With the proposition that the sum of k (k<=n+1) polynomial functions on n always yields a polynomial function, we prove that P=NP, considering the maximum clique problem. And with the proposition that the sum of k polynomial functions may yield an exponential function, we prove that P!=NP by constructing an abstract decision problem. Furthermore, we conclude that P=NP and P!=NP if and only if the above propositions hold, respectively.

Comments: 5 Pages. This is a short and interesting paper.

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Submission history

[v1] 2015-02-01 04:19:35
[v2] 2015-02-07 01:36:11
[v3] 2015-02-07 06:24:59

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