P VS NP it技术 - 锐客网

丈夫志四海，万里犹比邻。这篇文章主要讲述P VS NP相关的知识，希望能为你提供帮助。

目录

1.1 P
- 1.1.1 NP
- 1.1.2 Certifiers and certificates: satisfiability
2.1 Certifiers and certificates: Hamilton path
- 2.1.1 Some problems in NP
3.1 P, NP, and EXP
- 3.1.1 The main question: P vs. NP

1.1 PDef. Algorithm A runs in polynomial time if for every string s, A(s)
terminates in ≤ p( ?s?) “steps,” where p(?) is some polynomial function.
1.1.1 NP
Def. Algorithm C(s, t) is a certifier for problem X if for every string s : s ∈ X iff there exists a string t such that C(s, t) = yes.
NP = set of decision problems for which there exists a poly-time certifier.
?C(s, t) is a poly-time algorithm.
?Certificate t is of polynomial size: ?t? ≤ p(?s?) for some polynomial p(?)
关于NP举一个例子：

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我们找是否有两个数相乘等于437669
首先我们找到了一个可验证的解就是541
那么只要我们可以找多项式时间内找到809我们就可以找到原问题的解。

1.1.2 Certifiers and certificates: satisfiability

3-SAT. SAT where each clause contains exactly 3 literals.
Certificate. An assignment of truth values to the Boolean variables.
Certifier. Check that each clause in Φ has at least one true literal.

验证步骤是这样的：

首先我们找到其中一个解作为验证实例比如x1=true,x2=tru2,x3=false,x4=false;
我们必须在多项式时间内可以验证这个解是成立的！

2.1 Certifiers and certificates: Hamilton path【P VS NP】HAMILTON-PATH： Given an undirected graph G = (V, E), does there exist a
simple path P that visits every node?
Certificate： A permutation π of the n nodes.
Certifier： Check that π contains each node in V exactly once,
and that G contains an edge between each pair of adjacent nodes
2.1.1 Some problems in NP

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3.1 P, NP, and EXPP. Decision problems for which there exists a poly-time algorithm.
NP. Decision problems for which there exists a poly-time certifier.
EXP. Decision problems for which there exists an exponential-time algorithm.
3.1.1 The main question: P vs. NP
Does P = NP? [Cook 1971, Edmonds, Levin, Yablonski, G?del]
Is the decision problem as easy as the certification problem?