User:BrittMoon89/sandbox

P Versus NP

The Question Is whether or not, for all problems for which an algorithm can verify a given solution quickly (that is, in Polynomial time), an algorithm can also find that solution quickly.

NP stand for in NP complete non-deterministic Polynomial A problem is called NP(non-deterministic Polynomial) if its solution can be guessed and verified in Polynomial time; non-deterministic means that no particular rule is followed to make the guess. If a problem is NP and all other NP problems are Polynomial - time reducible to it, the problem is NP-complete.

NP(complexity) In computational complexity theory, NP (non-deterministic Polynomial time) is a complexity class used to classify decision problems.

The equivalent definition of NP is the set of decision problems solvable in Polynomial time by a non - deterministic Turing machine.

NP "non-deterministic, Polynomial time"

NP - Decision problems on the fastest known algorithms which are also based on assigned complexity classes.

If a problem is solvable in Polynomial time then a solution is also verifiable in Polynomial time by simply solving the problem.

Poly-logarithmic time An algorithm is said to run if T(n)=O((log n) to the k power), for some constant k.

Formulas 2 to the o power in multiple with (log n) = n to the 2nd power + n, n to the 10th power equals P. NTIME(n to the k power) = O(n to the k power) equals NP

P= NP complete

P = O(n to the k power)

P = NP complete = NP