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The complexity class # P was first defined by Leslie Valiant in a 1979 paper on the computation of the permanent, in which he proved that permanent is # P-complete.
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complexity and class
* AM, a complexity class related to Arthur – Merlin protocol
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.
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.
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:
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.
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 #
# REDIRECT Computational complexity theory
# All mathematical aspects of computer science, including complexity theory, logic of programming languages, analysis of algorithms, cryptography, computer vision, pattern recognition, information processing and modelling of intelligence.
In computational complexity theory, the complexity class # P ( pronounced " number P " or, sometimes " sharp P " or " hash P ") is the set of the counting problems associated with the decision problems in the set NP.
# P-complete, pronounced " sharp P complete " or " number P complete " is a complexity class in computational complexity theory.
# Test that F ≠ N, that F divides N ( time complexity O ( log N )), and that F is prime ( polynomial time ; see AKS primality test ).
# REDIRECT time complexity # Polynomial time
# REDIRECT time complexity
# REDIRECT Quantum complexity theory
# REDIRECT Kolmogorov complexity
# It required greater mechanical complexity of the player.
# Manufacturing complexity
# REDIRECT Computational complexity theory
# simplicity ( S. niṣprapāncha, T. spros bral ) " free from complexity " or " not elaborate.
# REDIRECT Time complexity # Linearithmic / quasilinear time
* Time complexity # Linearithmic / quasilinear time
# Along with higher relative prices for energy, higher overall complexity and total costs for regulatory oversight, tariff administration, and metering and billing.
# redirect Irreducible complexity
# REDIRECT Game complexity
complexity and P
Provided that the complexity classes P and NP are not equal, none of these restrictions are NP-complete, unlike SAT.
Diagram of complexity classes provided that P ≠ NP.
Currently, one of the most famous open problems in theoretical computer science is the P = NP problem, which involves the relationship between the complexity classes P and NP.
It is suspected to be outside of all three of the complexity classes P, NP-complete, and co-NP-complete.
Euler diagram for P ( complexity ) | P, NP, NP-complete, and NP-hard set of problems.
The most important open question in complexity theory, the P = NP problem, asks whether polynomial time algorithms actually exist for NP-complete, and by corollary, all NP problems.
Oracle machines are useful for investigating the relationship between complexity classes P and NP, by considering the relationship between P < sup > A </ sup > and NP < sup > A </ sup > for an oracle A.
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