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# 7/18/2019 - The Better Minor Piece

NP!

I presume you are conscious of the fact that NP can stand for non-deterministic polynomial time, having vast applications in computer science. In particular, the P versus NP problem has baffled some of the world's most curious and intellectual minds.

The essence of the P versus NP problem, as stated verbatim by Clay Mathematics Institute, is: If it is easy to check that a solution to a problem is correct, is it also easy to solve the problem? Understanding the question itself should seem relatively self-explanatory, but once you delve into the more intricate aspects of it, you begin to realise the profound implications of computational complexity theory. Interestingly, it is closely related to Hamiltonian path problems, which are of great importance in graph theory. NP is the class of questions for which an answer can be verified in non polynomial time, while P is the class of questions for which some algorithm can verify an answer in polynomial time. A common misconception, however, is that P refers to something easy, which is not exactly the case. This erroneous presumption gives rise to something known Cobham's thesis. Obviously, I am unable to explain it thoroughly in detail here, but I vastly encourage one at their own cost of insatiable curiosity to view the following link:

https://en.wikipedia.org/wiki/P_versus_NP_problem#