英语博客：Nondeterminism and NP Theory（不确定性和NP理论） 已有 412 次阅读 2017-8-25 05:50 |个人分类:不确定性问题和算法讨论|系统分类:科研笔记|

英语博客：Nondeterminism and NP Theory（不确定性和NP理论）

已有 412 次阅读 2017-8-25 05:50 |个人分类:不确定性问题和算法讨论|系统分类:科研笔记|关键词:英语博客

最近德国波恩大学的计算机科学家Nobert Blum声称证明了“P/=NP” [1]，再次引发学术界对世纪难题“P vs NP”的关注与讨论。事实上，此问题不仅是计算机理论的基本问题，更与如今蓬勃发展的人工智能的基本理论问题密切相关。

“P vs NP”反应的是计算机领域最基本的“确定性问题与不确定性问题”的关系问题，然而由于流行的NP定义中“不确定性”的消失，使得“P vs NP”问题的研究始终处于停止不前的状态，我们已博客中与大家一起讨论了与此相关的各种议题，今天我们又开通了英语博客“Nondeterminism and NP Theory （https://nptheory.blogspot.fr）”，希望在更大的范围内和国际同行进行更加广泛的讨论，欢迎大家一起参加！

［1］“最新证明面临质疑：P/NP问题为什么这么难？”（https://mp.weixin.qq.com/s?__biz=MzIyNDA2NTI4Mg==&mid=2655416878&idx=2&sn=4b9cb0389ec607144cf3f2ab748197d7&chksm=f3a67043c4d1f955349d9d89f27a21fa4a84961894ae92f5b8651cc8d98bd6cdba8c42540d61&mpshare=1&scene=1&srcid=0817CHhpQKADQfcTdnK3bKam&pass_ticket=Kqkmi0Mtv%2Ffif%2FVEir7fCFGAsY5uaty8u%2Bpl7JWf%2Fs%2FSO37P2u6wG6SuA3mUNGMv#rd）  

附英语博客的第一篇文章：

P versus NP － The Perplexity of "Nondeterminism"

août 24, 2017

- You can know the name of a bird in all the languages of the world, but when you're finished, you'll know absolutely nothing whatever about the bird. So let's look at the bird and see what it's doing - that's what counts. I learned very early the difference between knowing the name of something and knowing something.  (Richard P. Feynman)

- Things have their roots and branches, affairs have their end and beginning. When you know what comes first and what comes last, then you are near the "Tao". (The Great Learning "大学")

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The problem of "P versus NP" is said to be the most notorious problem in theoretical computer science, and it was designated as one of seven Millennium Problems by the Clay Mathematics Institute [1]. Although a lot of attempts have been done since it was put out, it remains an open century problem [2].

Recently the mathematics professor Norbert Blum from Bonn (Germany) claimed to solve it in his paper "A Solution of the P versus NP Problem", and now computer scientists around the world are examining his work [3]. In fact, this problem has also drawn attention to the lay people, for example, in May 2 2013, the New Yorker published an article entitled as "A Most Profound Math Problem" [4][5].

All these reflect the situation where the computer, specially the vigorous development of Artificial Intelligence, has brought profound changes and impacts into the contemporary society.

However, on the one hand, more and more people get interested in this problem, but on the other hand they become more and more confused, due to the fact that the understanding of this problem is always based on the existing theoretical framework, and they cannot really realize the true difficulty of the problem. In this sense, this problem is not only the curiosity of the public, but also the perplex of experts in computer science. Hemaspaandra expressed such perplex when he introduced Gasarch's second poll about "P versus NP" [6]:

- I hope that people in the distant future will look at these four articles to help get a sense of people’s thoughts back in the dark ages when P versus NP had not yet been resolved.

We think that the fundamental difficulty of "P versus NP" lies in NP's current definition where the property of "polynomial time verifiable" is used to define NP. Initially, NP was proposed to distinguish from P, speaking roughly, P designs some problems easy to solve while NP designs some problems difficult to solve. However, the property of "polynomial time verifiable" is by nature of "determinism" which makes the relationship between P and NP change from parallel one to inclusion one, and leads to the loss of "nondeterminism" from NP, consequently "P versus NP " become a paradox.

Peter Drucker, "the founder of modern management", said that “The most serious mistakes are not being made as a result of wrong answers. The true dangerous thing is asking the wrong question.” Then, why is the "problem" so important? Because the "problem" is the root of cognition and behavior of human, and the whole branches of thought and action are then developed from this root, that is, the definition of a "problem" is to create the realm which we face and deal with.

Such serious mistakes to ask the wrong question exist not only in the management decision-making, but also in all aspects in daily life. In some way, we can say that this is the biggest blind spot of human cognition. Therefore, we can say that the real difficulty of "P versus NP" is to ask "what is NP?" rather than to answer "whether is NP equals to P (NP = P)?"

We create this blog for the purpose  of providing a space of exchanging works about "P vs NP" coming from different reflexions for all peoples who work in this domain, and hope to contribute to the progress of this problem. Moreover, from a broader point of view, we hope to contribute to the integration of science and culture as well as Chinese and Western philosophy.

Reference :

[1] P vs NP Problem (http://www.claymath.org/millennium-problems/p-vs-np-problem)

[2] Stephen Cook, The complexity of theorem proving procedures. Proceedings of the Third Annual ACM Symposium on Theory of Computing. pp. 151-158 (1971). (http://theory.stanford.edu/~trevisan/cs172-07/cook.pdf)

[3] P-NP-PROBLEM : New attack on the biggest mystery of computer science (https://steemit.com/science/@n3bul4/p-np-problem-new-attack-on-the-biggest-mystery-of-computer-science)

[4] A Most Profound Math Problem (http://www.newyorker.com/tech/elements/a-most-profound-math-problem)

[5] The traduction of "A Most Profound Math Problem" in Chinese (http://blog.sciencenet.cn/blog-2322490-995211.html)

[6] The Second P =? NP Poll1 William I. Gasarch (http://www.cs.umd.edu/~gasarch/papers/poll2012.pdf)

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