Concepts inA complete problem for statistical zero knowledge
Zero-knowledge proof
In cryptography, a zero-knowledge proof or zero-knowledge protocol is an interactive method for one party to prove to another that a (usually mathematical) statement is true, without revealing anything other than the veracity of the statement.
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Mathematical proof
In mathematics, a proof is a demonstration that if some fundamental statements are assumed to be true, then some mathematical statement is necessarily true. Proofs are obtained from deductive reasoning, rather than from inductive or empirical arguments; a proof must demonstrate that a statement is always true (occasionally by listing all possible cases and showing that it holds in each), rather than enumerate many confirmatory cases.
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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. More formally, a problem p is called hard for a complexity class C under a given type of reduction, if there exists a reduction (of the given type) from any problem in C to p.
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Closure (mathematics)
A set has closure under an operation if performance of that operation on members of the set always produces a member of the same set. For example, the real numbers are closed under subtraction, but the natural numbers are not: 3 and 8 are both natural numbers, but the result of 3 − 8 is not a natural number. Another example is the set containing only the number zero, which is a closed set under multiplication.
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Promise problem
In computational complexity theory, a promise problem is a generalization of a decision problem where the input is promised to belong to a subset of all possible inputs. Unlike decision problems, the yes instances (the inputs for which an algorithm must return yes) and no instances do not exhaust the set of all inputs. Intuitively, the algorithm has been promised that the input does indeed belong to set of yes instances or no instances. There may be inputs which are neither yes or no.
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Bit
A bit (a contraction of binary digit) is the basic capacity of information in computing and telecommunications; a bit represents either 1 or 0 (one or zero) only. The representation may be implemented, in a variety of systems, by means of a two state device. In computing, a bit can be defined as a variable or computed quantity that can have only two possible values. These two values are often interpreted as binary digits and are usually denoted by the numerical digits 0 and 1.
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Class (set theory)
In set theory and its applications throughout mathematics, a class is a collection of sets (or sometimes other mathematical objects) which can be unambiguously defined by a property that all its members share. The precise definition of "class" depends on foundational context. In work on ZF set theory, the notion of class is informal, whereas other set theories, such as NBG set theory, axiomatize the notion of "class", e.g. , as entities that are not members of another entity.
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Statistically close
Let the statistical difference between two distributions and be defined as . We say that two probability ensembles and are statistically close if is a negligible function in . Statistical difference is based on the L1 norm.
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