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40 relations: Advice (complexity), Arthur–Merlin protocol, Boolean satisfiability problem, BPL (complexity), BPP, BQP, Church–Turing thesis, Circuits over sets of natural numbers, Complete (complexity), Complexity class, Computational complexity theory, Deutsch–Jozsa algorithm, Hard-core predicate, Interactive proof system, IP (complexity), Karp–Lipton theorem, List of complexity classes, List of terms relating to algorithms and data structures, List of unsolved problems in computer science, Low (complexity), Michael Sipser, Monte Carlo algorithm, P (complexity), P/poly, Parity P, PH (complexity), Polynomial hierarchy, PP (complexity), Probabilistic Turing machine, QIP (complexity), QMA, Quantum computing, Randomized algorithm, RP (complexity), Simon's problem, Sipser–Lautemann theorem, Structural complexity theory, Time complexity, Yao's test, ZPP (complexity).
Advice (complexity)
In computational complexity theory, an advice string is an extra input to a Turing machine that is allowed to depend on the length n of the input, but not on the input itself.
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Arthur–Merlin protocol
In computational complexity theory, an Arthur–Merlin protocol is an interactive proof system in which the verifier's coin tosses are constrained to be public (i.e. known to the prover too).
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Boolean satisfiability problem
In computer science, the Boolean satisfiability problem (sometimes called propositional satisfiability problem and abbreviated as SATISFIABILITY or SAT) is the problem of determining if there exists an interpretation that satisfies a given Boolean formula.
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BPL (complexity)
In computational complexity theory, BPL (Bounded-error Probabilistic Logarithmic-space), sometimes called BPLP (Bounded-error Probabilistic Logarithmic-space Polynomial-time), is the complexity class of problems solvable in logarithmic space and polynomial time with probabilistic Turing machines with two-sided error.
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BPP
BPP may refer to.
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BQP
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.
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Church–Turing thesis
In computability theory, the Church–Turing thesis (also known as computability thesis, the Turing–Church thesis, the Church–Turing conjecture, Church's thesis, Church's conjecture, and Turing's thesis) is a hypothesis about the nature of computable functions.
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Circuits over sets of natural numbers
Circuits over natural numbers are a mathematical model used in studying computational complexity theory.
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Complete (complexity)
In computational complexity theory, a computational problem is complete for a complexity class if it is, in a technical sense, among the "hardest" (or "most expressive") problems in the complexity class.
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Complexity class
In computational complexity theory, a complexity class is a set of problems of related resource-based complexity.
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Computational complexity theory
Computational complexity theory is a branch of the theory of computation in theoretical computer science that focuses on classifying computational problems according to their inherent difficulty, and relating those classes to each other.
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Deutsch–Jozsa algorithm
The Deutsch–Jozsa algorithm is a quantum algorithm, proposed by David Deutsch and Richard Jozsa in 1992 with improvements by Richard Cleve, Artur Ekert, Chiara Macchiavello, and Michele Mosca in 1998.
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Hard-core predicate
In cryptography, a hard-core predicate of a one-way function f is a predicate b (i.e., a function whose output is a single bit) which is easy to compute (as a function of x) but is hard to compute given f(x).
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Interactive proof system
In computational complexity theory, an interactive proof system is an abstract machine that models computation as the exchange of messages between two parties.
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IP (complexity)
In computational complexity theory, the class IP (which stands for Interactive Polynomial time) is the class of problems solvable by an interactive proof system.
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Karp–Lipton theorem
In complexity theory, the Karp–Lipton theorem states that if the Boolean satisfiability problem (SAT) can be solved by Boolean circuits with a polynomial number of logic gates, then That is, if we assume that NP, the class of nondeterministic polynomial time problems, can be contained in the non-uniform polynomial time complexity class P/poly, then this assumption implies the collapse of the polynomial hierarchy at its second level.
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List of complexity classes
This is a list of complexity classes in computational complexity theory.
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List of terms relating to algorithms and data structures
The NIST Dictionary of Algorithms and Data Structures is a reference work maintained by the U.S. National Institute of Standards and Technology.
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List of unsolved problems in computer science
This article is a list of unsolved problems in computer science.
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Low (complexity)
In computational complexity theory, a language B (or a complexity class B) is said to be low for a complexity class A (with some reasonable relativized version of A) if AB.
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Michael Sipser
Michael Fredric Sipser (born September 17, 1954) is a theoretical computer scientist who has made early contributions to computational complexity theory.
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Monte Carlo algorithm
In computing, a Monte Carlo algorithm is a randomized algorithm whose output may be incorrect with a certain (typically small) probability.
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P (complexity)
In computational complexity theory, P, also known as PTIME or DTIME(nO(1)), is a fundamental complexity class.
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P/poly
In computational complexity theory, P/poly is the complexity class of languages recognized by a polynomial-time Turing machine with a polynomial-bounded advice function.
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Parity P
In computational complexity theory, the complexity class ⊕P (pronounced "parity P") is the class of decision problems solvable by a nondeterministic Turing machine in polynomial time, where the acceptance condition is that the number of accepting computation paths is odd.
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PH (complexity)
In computational complexity theory, the complexity class PH is the union of all complexity classes in the polynomial hierarchy: PH was first defined by Larry Stockmeyer.
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Polynomial hierarchy
In computational complexity theory, the polynomial hierarchy (sometimes called the polynomial-time hierarchy) is a hierarchy of complexity classes that generalize the classes P, NP and co-NP to oracle machines.
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PP (complexity)
In complexity theory, PP is the class of decision problems solvable by a probabilistic Turing machine in polynomial time, with an error probability of less than 1/2 for all instances.
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Probabilistic Turing machine
In computability theory, a probabilistic Turing machine is a non-deterministic Turing machine which chooses between the available transitions at each point according to some probability distribution.
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QIP (complexity)
In computational complexity theory, the class QIP, which stands for Quantum Interactive Polynomial time, is the quantum computing analogue of the classical complexity class IP, which is the set of problems solvable by an interactive proof system with a polynomial-time verifier and one computationally unbounded prover.
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QMA
In computational complexity theory, QMA, which stands for Quantum Merlin Arthur, is the quantum analog of the nonprobabilistic complexity class NP or the probabilistic complexity class MA.
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Quantum computing
Quantum computing is computing using quantum-mechanical phenomena, such as superposition and entanglement.
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Randomized algorithm
A randomized algorithm is an algorithm that employs a degree of randomness as part of its logic.
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RP (complexity)
In computational complexity theory, randomized polynomial time (RP) is the complexity class of problems for which a probabilistic Turing machine exists with these properties.
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Simon's problem
In computational complexity theory and quantum computing, Simon's problem is a computational problem that can be solved exponentially faster on a quantum computer than on a classical (or traditional) computer.
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Sipser–Lautemann theorem
In computational complexity theory, the Sipser–Lautemann theorem or Sipser–Gács–Lautemann theorem states that bounded-error probabilistic polynomial (BPP) time is contained in the polynomial time hierarchy, and more specifically Σ2 ∩ Π2.
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Structural complexity theory
In computational complexity theory of computer science, the structural complexity theory or simply structural complexity is the study of complexity classes, rather than computational complexity of individual problems and algorithms.
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Time complexity
In computer science, the time complexity is the computational complexity that describes the amount of time it takes to run an algorithm.
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Yao's test
In cryptography and the theory of computation, Yao's test is a test defined by Andrew Chi-Chih Yao in 1982,Andrew Chi-Chih Yao.
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ZPP (complexity)
In complexity theory, ZPP (zero-error probabilistic polynomial time) is the complexity class of problems for which a probabilistic Turing machine exists with these properties.
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Redirects here:
BPP (complexity class), Bounded error probability in polynomial time, Bounded-error probabilistic polynomial, P = BPP problem.
References
[1] https://en.wikipedia.org/wiki/BPP_(complexity)
