On the Approximation Method and the P versus NP Problem

2017/08/11 by Norbert Blum, Norbert Blüm, Blum, Norbert · 3 voices
Computer Science · Mathematics · #Combinatorics #Computer science #Fuzzy Logic and Control Systems #Mathematics #cs.CC

paper · pdf · doi:10.48550/arxiv.1708.03486

The paper is the replacement of the incorrect paper "A Solution of the P versus NP Problem"

openalex publication_date 2017/08/11 · arxiv created 2020/06/15 · arxiv updated 2020/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

First of all we give some reasons that "natural proofs" built not a barrier to prove P \not= NP using Boolean complexity. Then we investigate the approximation method for its extension to prove super-polynomial lower bounds for the non-monotone complexity of suitable Boolean functions in NP or to understand why this is not possible. It is given some evidence that the approximation method alone cannot be used to prove a super-linear lower bound for any function f ∈ \cal B_n. Additionally, an overview on the methods for proving lower bounds of the non-monotone and the monotone complexity of Boolean functions is given. Finally, a personal opinion how to proceed the research on the P versus NP problem and also on proving a super-linear lower bound for the non-monotone complexity of a Boolean function in NP is given.

Discussions

• A Solution of the P versus NP Problem? [hn, 662 points, 286 comments]
• Blum: “The proof is wrong. I shall elaborate precisely what the mistake is.” [hn, 258 points, 78 comments]
• A Solution of the P versus NP Problem [lobsters, 59 points, 14 comments]

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