##### The Collaborative International Dictionary

**Np**

Np \Np\ n. The chemical symbol for Neptunium, a transuranic element having atomic number 93.

Syn: Neptunium, atomic number 93.

##### Wiktionary

**np**

abbr. 1 (context text messaging Internet English) no problem; it was nothing; it's ok; don't mention it; you're welcome. 2 no pagination 3 no place (of publication)

##### Wikipedia

**NP (complexity)**

In computational complexity theory, **NP** is a complexity class used to describe certain types of decision problems. Informally, **NP** is the set of all decision problems for which the instances where the answer is "yes" have efficiently *verifiable* proofs. More precisely, these proofs have to be verifiable by deterministic computations that can be performed in polynomial time.

Equivalently, the formal definition of **NP** is the set of decision problems *solvable* in polynomial time by a theoretical non-deterministic Turing machine. This second definition is the basis for the abbreviation **NP**, which stands for " nondeterministic, polynomial time." However, the *verifier-based definition* tends to be more intuitive and practical in common applications compared to the formal *machine definition*. The two definitions are equivalent because the algorithm for the machine definition consists of two phases, the first of which consists of a guess about the solution, which is generated in a non-deterministic way, while the second phase consists of a deterministic algorithm that verifies or rejects the guess as a valid solution to the problem.

A method for solving a decision problem is given in the form of an algorithm. In the above definitions for **NP**, *polynomial time* refers to the increasing number of machine operations needed by an algorithm relative to the size of the problem. Polynomial time is therefore a measure of efficiency of an algorithm. Decision problems are commonly categorized into complexity classes (such as **NP**) based on the fastest known machine algorithms. As such, decision problems may change class if a faster algorithm is discovered.

The complexity class ** P** is contained in **NP**, but **NP** contains many important problems, the hardest of which are called NP-complete problems, whose solutions are sufficient to deal with any other NP problem in polynomial time. The most important open question in complexity theory, the P versus NP ("P=NP") problem, asks whether polynomial time algorithms actually exist for solving **NP**-complete, and by corollary, all **NP** problems. It is widely believed that this is not the case.

The complexity class **NP** (which have efficiently verifiable proofs where the answer is "yes") is also related to the complexity class ** co-NP** (which have efficiently verifiable proofs where the answer is "no"). Whether or not **NP** = **co-NP** is another outstanding question in complexity theory.

**NP**

**NP** may refer to:

#### Usage examples of "np".

Since several nations were still trying to obtain them, the extension of __NPT__ was one of my most important nonproliferation objectives.

His long arms, encased in __NPS__ green, semaphored information and enthusiasm.

__NPT__, possibly because the polo and sports car afficionado with the posh accent lacks the diplomatic gloss appropriate to this sensitive enterprise.

Muscular hips and legs gave her a stocky silhouette that was accentuated by the flat-brimmed hat and cloddy shoes of the __NPS__ uniform she wore on duty.