Concepts inThe average-case complexity of counting distinct elements

Average-case complexity

Average-case complexity is a subfield of computational complexity theory that studies the complexity of algorithms on random inputs. The study of average-case complexity has applications in the theory of cryptography. Leonid Levin presented the motivation for studying average-case complexity as follows:: "Many combinatorial problems (called search or NP problems) have easy methods of checking solutions for correctness.
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Counting

Counting is the action of finding the number of elements of a finite set of objects.
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Chemical element

A chemical element is a pure chemical substance consisting of one type of atom distinguished by its atomic number, which is the number of protons in its nucleus. They are divided into metals and non-metals. Familiar examples of elements include carbon, oxygen (non-metals) together with aluminium, iron, copper, gold, mercury, and lead (metals). As of November 2011, 118 elements have been identified, the latest being ununseptium in 2010.
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Data stream

In telecommunications and computing, a data stream is a sequence of digitally encoded coherent signals used to transmit or receive information that is in the process of being transmitted. In electronics and computer architecture, a data flow determines for which time which data item is scheduled to enter or leave which port of a systolic array, a Reconfigurable Data Path Array or similar pipe network, or other processing unit or block.
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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 andÂ 1.
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Structure (mathematical logic)

In universal algebra and in model theory, a structure consists of a set along with a collection of finitary operations and relations which are defined on it. Universal algebra studies structures that generalize the algebraic structures such as groups, rings, fields and vector spaces. The term universal algebra is used for structures with no relation symbols.
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