complexity class

Several natural complexity classes are known to be low for themselves.

It is the quantum analogue of the complexity class P.

Many complexity classes are defined using the concept of a reduction.

This motivates the concept of a problem being hard for a complexity class.

This is mandatory for complexity classes using less than linear time.

When talking about complexity classes, a worst case scenario is usually assumed.

Thus there are pairs of complexity classes such that one is properly included in the other.

The complexity class is defined to be equal to .

Currently the main focus of the program is on algebraic complexity classes.

Of course, some complexity classes have complex definitions that do not fit into this framework.

Thus, a typical complexity class has a definition like the following:

Many circuit complexity classes are defined in terms of class hierarchies.

Therefore, the appropriate notion of reduction depends on the complexity class being studied.

The problem can be of any complexity class.

Many known complexity classes are suspected to be unequal, but this has not been proved.

The W hierarchy is a collection of computational complexity classes.

P is one of the largest complexity classes considered "computationally feasible".

Let us assume that H is in this time complexity class, and we will attempt to reach a contradiction.

Valiant's 1979 paper also introduced as a complexity class.

Some important complexity classes of decision problems defined in this manner are the following:

Several important space complexity classes are sublinear, that is, smaller than the size of the input.

Function problems can be sorted into complexity classes in the same way as decision problems.

For complexity classes larger than P, polynomial-time reductions are commonly used.

Unfortunately, this fact doesn't say much about where the problem lies with respect to non-quantum complexity classes.

When the class of authorized gate is restricted, the membership problem lay inside well known complexity classes.