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In complexity theory, the class NC ( for " Nick's Class ") is the set of decision problems decidable in polylogarithmic time on a parallel computer with a polynomial number of processors.
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complexity and theory
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In algorithmic information theory ( a subfield of computer science ), the Kolmogorov complexity of an object, such as a piece of text, is a measure of the computational resources needed to specify the object.
Kolmogorov complexity is also known as " descriptive complexity " ( not to be confused with descriptive complexity theory ), Kolmogorov – Chaitin complexity, algorithmic entropy, or program-size complexity.
Algorithmic information theory is the area of computer science that studies Kolmogorov complexity and other complexity measures on strings ( or other data structures ).
Algorithm analysis is an important part of a broader computational complexity theory, which provides theoretical estimates for the resources needed by any algorithm which solves a given computational problem.
The term was coined by Fanya Montalvo by analogy with NP-complete and NP-hard in complexity theory, which formally describes the most famous class of difficult problems.
Computational complexity theory deals with the relative computational difficulty of computable functions.
Since many AI problems have no formalisation yet, conventional complexity theory does not allow the definition of AI-completeness.
To address this problem, a complexity theory for AI has been proposed.
In computational complexity theory, BPP, which stands for bounded-error probabilistic polynomial time is the class of decision problems solvable by a probabilistic Turing machine in polynomial time, with an error probability of at most 1 / 3 for all instances.
In computational complexity theory, BQP ( bounded error quantum polynomial time ) is the class of decision problems solvable by a quantum computer in polynomial time, with an error probability of at most 1 / 3 for all instances.
Category: Quantum complexity theory
In complexity theory, the satisfiability problem ( SAT ) is a decision problem, whose instance is a Boolean expression written using only AND, OR, NOT, variables, and parentheses.
This property is used in several theorems in complexity theory:
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complexity and class
* AM, a complexity class related to Arthur – Merlin protocol
It is the quantum analogue of the complexity class BPP.
Detailed analysis shows that the complexity class is unchanged by allowing error as high as 1 / 2 − n < sup >− c </ sup > on the one hand, or requiring error as small as 2 < sup >− n < sup > c </ sup ></ sup > on the other hand, where c is any positive constant, and n is the length of input.
Adding postselection to BQP results in the complexity class PostBQP which is equal to PP.
In computational complexity theory, co-NP is a complexity class.
A problem is a member of co-NP if and only if its complement is in the complexity class NP.
* Complexity class, a set of problems of related complexity in computational complexity theory
A famous network of conditional proofs is the NP-complete class of complexity theory.
* IP ( complexity ), a class in computational complexity theory
It is therefore a candidate for the NP-intermediate complexity class.
The complexity class P is contained in NP, but NP contains many important problems, the hardest of which are called NP-complete problems, for which no polynomial-time algorithms are known for solving them ( although they can be verified in polynomial time ).
The complexity class NP can be defined in terms of NTIME as follows:
The problem can be of any complexity class.
The complexity class of decision problems solvable by an algorithm in class A with an oracle for a language L is called A < sup > L </ sup >.
The notation A < sup > B </ sup > can be extended to a set of languages B ( or a complexity class B ), by using the following definition:
BQP is contained in the complexity class # P ( or more precisely in the associated class of decision problems P < sup ># P </ sup >), which is a subclass of PSPACE.
complexity and NC
One major open question in complexity theory is whether or not every containment in the NC hierarchy is proper.
* NC a complexity class named after Nick Pippenger
* NC ( complexity ) Nick's Class, the set of decision problems decidable in polylogarithmic time on a parallel computer with a polynomial number of processors
The complexity class, Nick's Class ( NC ), of problems quickly solvable on a parallel computer, was named by Stephen Cook after Nick Pippenger for his research on circuits with polylogarithmic depth and polynomial size.
# REDIRECT NC ( complexity )
In circuit complexity, NL can be placed within the NC hierarchy.
If NC is a complexity class associated with non-deterministic machines then # C =
0.193 seconds.