Concepts inData correspondence, exchange and repair
Tuple
In mathematics and computer science, a tuple is an ordered list of elements. In set theory, an (ordered) -tuple is a sequence (or ordered list) of elements, where is a positive integer. There is also one 0-tuple, an empty sequence. An -tuple is defined inductively using the construction of an ordered pair. Tuples are usually written by listing the elements within parentheses "" and separated by commas; for example, denotes a 5-tuple.
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Directed acyclic graph
In mathematics and computer science, a directed acyclic graph, is a directed graph with no directed cycles. That is, it is formed by a collection of vertices and directed edges, each edge connecting one vertex to another, such that there is no way to start at some vertex v and follow a sequence of edges that eventually loops back to v again. DAGs may be used to model several different kinds of structure in mathematics and computer science.
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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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Database
A database is an organized collection of data, today typically in digital form. The data are typically organized to model relevant aspects of reality (for example, the availability of rooms in hotels), in a way that supports processes requiring this information (for example, finding a hotel with vacancies). The term database is correctly applied to the data and their supporting data structures, and not to the database management system (DBMS).
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Data exchange
Data exchange is the process of taking data structured under a source schema and actually transforming it into data structured under a target schema, so that the target data is an accurate representation of the source data. Data exchange is similar to the related concept of data integration except that data is actually restructured (with possible loss of content) in data exchange. There may be no way to transform an instance given all of our constraints.
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Homomorphism
In abstract algebra, a homomorphism is a structure-preserving map between two algebraic structures. The word homomorphism comes from the ancient Greek language: ¿¿¿¿ (homos) meaning "same" and ¿¿¿¿¿ (morphe) meaning "shape". Isomorphisms, automorphisms, and endomorphisms are all types of homomorphism.
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