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Encyclopedia > Complexity class

In computational complexity theory, a complexity class is a set of problems of related complexity. A typical complexity class has a definition of the form:

the set of problems that can be solved by abstract machine M using O(f(n)) of resource R (n is the size of the input)

For example, the class NP is the set of decision problems that can be solved by a non-deterministic Turing machine in polynomial time, while the class PSPACE is the set of decision problems that can be solved by a deterministic Turing machine in polynomial space. Some complexity classes are sets of function problems, such as FP.


Many complexity classes can be characterized in terms of the mathematical logic needed to express them; see descriptive complexity.


See also: List of complexity classes



Important complexity classes (more)
P | NP | Co-NP | NP-C | Co-NP-C | NP-hard | UP | #P | #P-C | L | NC | P-C
PSPACE | PSPACE-C | EXPTIME | EXPSPACE | BQP | BPP | RP | ZPP | PCP | IP | PH

  Results from FactBites:
 
Computational complexity theory - Wikipedia, the free encyclopedia (1129 words)
Complexity theory is part of the theory of computation dealing with the resources required during computation to solve a given problem.
The time complexity of a problem is the number of steps that it takes to solve an instance of the problem as a function of the size of the input (usually measured in bits), using the most efficient algorithm.
The complexity class P is the set of decision problems that can be solved by a deterministic machine in polynomial time.
Complexity class - definition of Complexity class in Encyclopedia (161 words)
In computational complexity theory, a complexity class is a set of problems of related complexity.
For example, the class NP is the set of decision problems that can be solved by a non-deterministic Turing machine in polynomial time, while the class PSPACE is the set of decision problems that can be solved by a deterministic Turing machine in polynomial space.
Some complexity classes are sets of function problems, such as FP.
  More results at FactBites »


 

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