Although the P versus NP Question remains unresolved, the theory of NP-completeness offers evidence for the intractability of specific problems in NP by showing that they are universal for the entire class. Amazingly enough, NP-complete problems exist, and furthermore hundreds of natural ...
序列化和反序列化 # 把所有图片解析成一个矩阵,然后保存到一个二进制文件,然后读取二进制文件还原成图片 class Image_Array_Util(object): __arrayFile...,)) image_arr=np.concatenate((r_arr,g_arr,b_arr)) #image_arr矩阵==一张图片 big_arr=np.concatenate((big_arr,image_arr NP completeness(NP...
NP-completeness has been the core concept of computational complexity theory. NP-complete problems are defined by reductions, which is instrumental in establishing the tower of computational complexity theory. Yet, reductions depend on skills and vary among problems, lacking a unified pattern...
到这为止NP-hardness和NP-completeness就很好理解了。称问题L是NP-hard，如果任意一个NP的问题都可以多项...
Although this claim looks very plausible and intuitive, currently we cannot provide a definite answer for it. However, we can solve in the affirmative a weaker claim that says that all ``consistent'' universal first-order sentences can be safely eliminated without the fear of losing completeness...
Response: There's a good theoretical answer to this: it's because polynomials are the smallest class of functions that contains the linear functions, and that's closed under basic operations like addition, multiplication, and composition. For this reason, they're the smallest class that ensures ...
¶We draw several observations and relationships between the following two properties of a complexity class C: whether there exists a truthtable hard p-selective language for C, and whether polynomially-many nonadaptive queries to C can be answered by making O(log n)-many adaptive queries to ...
NP hard is a bit of an odd class, and it doesn't come up as much as the others. What if P = NP? So, does P equal NP? It's still an open question, but most researchers think P doesn't equal NP. Given the number of NP complete problems and the fact that they cross ...
NP-Completeness As it turns out, the problems of 3-Satisfiability and k-Clique are quite special (as is graph coloring). They belong to a special sub-class of NP called NP-complete. Before we can define what NP-complete means, we have to be able to compare problems in NP. ...
So by the Completeness Theorem, ZF + Con (ZF) has a model. What on earth could it be? We'll answer this question via a fictional dialogue between you and the axioms of ZF + Con (ZF). You: Look, you say ZF is inconsistent, from which it follows that there's a proof in ZF ...