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Arthur–Merlin protocol

Index 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). [1]

20 relations: Advice (complexity), BPP (complexity), Cambridge University Press, Complexity class, Computational complexity theory, Decision problem, Generalized Riemann hypothesis, Graph isomorphism problem, Interactive proof system, IP (complexity), NP (complexity), Oracle machine, Polynomial hierarchy, PP (complexity), PSPACE, QMA, Random number generation, S2P (complexity), Sipser–Lautemann theorem, Zero-knowledge proof.

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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BPP (complexity)

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 bounded away from 1/2 for all instances.

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Cambridge University Press

Cambridge University Press (CUP) is the publishing business of the University of Cambridge.

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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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Decision problem

In computability theory and computational complexity theory, a decision problem is a problem that can be posed as a yes-no question of the input values.

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Generalized Riemann hypothesis

The Riemann hypothesis is one of the most important conjectures in mathematics.

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Graph isomorphism problem

The graph isomorphism problem is the computational problem of determining whether two finite graphs are isomorphic.

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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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NP (complexity)

In computational complexity theory, NP (for nondeterministic polynomial time) is a complexity class used to describe certain types of decision problems.

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Oracle machine

In complexity theory and computability theory, an oracle machine is an abstract machine used to study decision problems.

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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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PSPACE

In computational complexity theory, PSPACE is the set of all decision problems that can be solved by a Turing machine using a polynomial amount of space.

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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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Random number generation

Random number generation is the generation of a sequence of numbers or symbols that cannot be reasonably predicted better than by a random chance, usually through a hardware random-number generator (RNG).

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S2P (complexity)

In computational complexity theory, S is a complexity class, intermediate between the first and second levels of the polynomial hierarchy.

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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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Zero-knowledge proof

In cryptography, a zero-knowledge proof or zero-knowledge protocol is a method by which one party (the prover Peggy) can prove to another party (the verifier Victor) that she knows a value x, without conveying any information apart from the fact that she knows the value x. Another way of understanding this would be: Interactive zero-knowledge proofs require interaction between the individual (or computer system) proving their knowledge and the individual validating the proof.

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Redirects here:

AM (complexity), Arthur-Merlin, Arthur-Merlin protocol, CoAM, MA (complexity), Merlin-Arthur protocol.

References

[1] https://en.wikipedia.org/wiki/Arthur–Merlin_protocol

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