# Complexity

NP (complexity) In computational complexity theory, NP is one of the most fundamental complexity classes.

The abbreviation NP refers to "nondeterministic polynomial time. " Intuitively, NP is the set of all decision problems for which the instances where the answer is "yes" have efficiently verifiable proofs of the fact that the answer is indeed "yes". Complexity class. In computational complexity theory, a complexity class is a set of problems of related resource-based complexity.

A typical complexity class has a definition of the form: the set of problems that can be solved by an abstract machine M using O(f(n)) of resource R, where n is the size of the input. The simpler complexity classes are defined by the following factors: Many complexity classes can be characterized in terms of the mathematical logic needed to express them; see descriptive complexity. Computational complexity theory. Computational complexity theory is a branch of the theory of computation in theoretical computer science and mathematics that focuses on classifying computational problems according to their inherent difficulty, and relating those classes to each other.

A computational problem is understood to be a task that is in principle amenable to being solved by a computer, which is equivalent to stating that the problem may be solved by mechanical application of mathematical steps, such as an algorithm. A problem is regarded as inherently difficult if its solution requires significant resources, whatever the algorithm used.

Abstract machine. An abstract machine, also called an abstract computer, is a theoretical model of a computer hardware or software system used in automata theory.

Abstraction of computing processes is used in both the computer science and computer engineering disciplines and usually assumes discrete time paradigm. Information[edit] In the theory of computation, abstract machines are often used in thought experiments regarding computability or to analyze the complexity of algorithms (see computational complexity theory).