Saturday, August 8, 2020

### What is P=NP?

Wikipedia describes P=NP as the following:

The P versus NP problem is a major unsolved problem in computer science. It asks whether every problem whose solution can be quickly verified (technically, verified in polynomial time) can also be solved quickly (again, in polynomial time). It is one of the seven Millennium Prize Problems selected by the Clay Mathematics Institute.

The informal term quickly used above, means the existence of an algorithm solving the task that runs in polynomial time, such that the time to complete the task varies as a polynomial function on the size of the input to the algorithm (as opposed to, say, exponential time). The general class of questions for which some algorithm can provide an answer in polynomial time is called “class P” or just “P”.

For some questions, there is no known way to find an answer quickly, but if one is provided with information showing what the answer is, it is possible to verify the answer quickly. The class of questions for which an answer can be verified in polynomial time is called NP, which stands for “nondeterministic polynomial time”. An answer to the P = NP question would determine whether problems that can be verified in polynomial time can also be solved in polynomial time. If it turned out that P ≠ NP, it would mean that there are problems in NP that are harder to compute than to verify: they could not be solved in polynomial time, but the answer could be verified in polynomial time.

Aside from being an important problem in computational theory, a proof either way would have profound implications for mathematics, cryptography, algorithm research, artificial intelligence, game theory, multimedia processing, philosophy, economics and many other fields.

The Fuzzy.One Solution

After years of research, we claim to have found a philosophical solution to the P = NP problem.

Our statement is that P = NP is a binary environment problem. This means that the problem of P = NP is only found where there is only one correct answer. Such as solving a code in cryptography.
However, in a non binary environment, as in decision-making process’ there is not just one solution, the environment is fuzzy, not binary, therefore there is always a complexity that separates the binary P = NP universe from the fuzzy or non-binary universe.

In other words, P = NP is a binary concept for handling binary problems.

With this in mind, we do accept that P = NP is applicable to everyday life situations, where solving a problem can take longer than validating the solution since there is most probably many viable solutions for one problem.

In other words; can we reduce the probability of selecting the “wrong” solution, or in most cases the “not most efficient” solution and enable us to select the “correct” solution or “most efficient” solution from a list of validated solutions.