11 Facts About Complexity class

In computational complexity theory, a complexity class is a set of computational problems of related resource-based complexity.

In general, a complexity class is defined in terms of a type of computational problem, a model of computation, and a bounded resource like time or memory.

For instance, the Complexity class P is the set of decision problems solvable by a deterministic Turing machine in polynomial time.

The complexity class P is defined as the set of decision problems that can be solved by a deterministic Turing machine in polynomial time.

The amount of time it takes to solve problems in the complexity class P grows at a polynomial rate as the input size increases, which is comparatively slow compared to problems in the exponential complexity class EXPTIME .

An important characteristic of the Complexity class NP is that it can be equivalently defined as the Complexity class of problems whose solutions are verifiable by a deterministic Turing machine in polynomial time.

Strictest Complexity class is ZPP, the Complexity class of problems solvable in polynomial time by a probabilistic Turing machine with error probability 0.

Slightly looser Complexity class is RP, which maintains no error for strings not in the language but allows bounded error for strings in the language.

The Complexity class co-RP is similarly defined except the roles are flipped: error is not allowed for strings in the language but is allowed for strings not in the language.

The Complexity class NC is the set of languages that can be solved by circuit families that are restricted not only to having polynomial-size but to having polylogarithmic depth.

The Complexity class AC is defined similarly to NC, however gates are allowed to have unbounded fan-in .