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Dependency Theory (database Theory)
Dependency theory is a subfield of database theory which studies implication and optimization problems related to logical constraints, commonly called dependencies, on databases. The best known class of such dependencies are functional dependencies, which form the foundation of keys on database relations. Another important class of dependencies are the multivalued dependencies. A key algorithm in dependency theory is the chase, and much of the theory is devoted to its study. Dependencies * functional dependency * join dependency * multivalued dependency * tuple-generating dependency In relational database theory, a tuple-generating dependency (TGD) is a certain kind of constraint on a relational database. It is a subclass of the class of embedded dependencies (EDs). An algorithm known as the chase takes as input an instance ... * equality-generating dependency * embedded dependency * inclusion dependency * full typed dependency {{database-stub Database theory Datab ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Database Theory
Database theory encapsulates a broad range of topics related to the study and research of the theoretical realm of databases and database management systems. Theoretical aspects of data management include, among other areas, the foundations of query languages, computational complexity and expressive power of queries, finite model theory, database design theory, dependency theory, foundations of concurrency control and database recovery, deductive databases, temporal and spatial databases, real-time databases, managing uncertain data and probabilistic databases, and Web data. Most research work has traditionally been based on the relational model, since this model is usually considered the simplest and most foundational model of interest. Corresponding results for other data models, such as object-oriented or semi-structured models, or, more recently, graph data models and XML, are often derivable from those for the relational model. A central focus of database theory is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Functional Dependency
In relational database theory, a functional dependency is a constraint between two sets of attributes in a relation from a database. In other words, a functional dependency is a constraint between two attributes in a relation. Given a relation ''R'' and sets of attributes X,Y \subseteq R, ''X'' is said to functionally determine ''Y'' (written ''X'' → ''Y'') if and only if each ''X'' value in ''R'' is associated with precisely one ''Y'' value in ''R''; ''R'' is then said to ''satisfy'' the functional dependency ''X'' → ''Y''. Equivalently, the projection \Pi_R is a function, i.e. ''Y'' is a function of ''X''. In simple words, if the values for the ''X'' attributes are known (say they are ''x''), then the values for the ''Y'' attributes corresponding to ''x'' can be determined by looking them up in ''any'' tuple of ''R'' containing ''x''. Customarily ''X'' is called the ''determinant'' set and ''Y'' the ''dependent'' set. A functional dependency FD: ''X'' → ''Y'' is called ''tr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Candidate Key
A candidate key, or simply a key, of a relational database is a minimal superkey. In other words, it is any set of columns that have a unique combination of values in each row (which makes it a superkey), with the additional constraint that removing any column would possibly produce duplicate rows (which makes it a minimal superkey). Specific candidate keys are sometimes called primary keys, secondary keys or alternate keys. The columns in a candidate key are called prime attributes, and a column that does not occur in any candidate key is called a non-prime attribute. Every relation without NULL values will have at least one candidate key: Since there cannot be duplicate rows, the set of all columns is a superkey, and if that isn't minimal, some subset of that will be minimal. There is a functional dependency from the candidate key to all the attributes in the relation. The candidate keys of a relation are all the possible ways we can identify a row. As such, they are an impo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multivalued Dependency
In database theory, a multivalued dependency is a full constraint between two sets of attributes in a relation. In contrast to the functional dependency, the multivalued dependency requires that certain tuples be present in a relation. Therefore, a multivalued dependency is a special case of ''tuple-generating dependency''. The multivalued dependency plays a role in the 4NF database normalization. A multivalued dependency is a special case of a join dependency, with only two sets of values involved, i.e. it is a binary join dependency. A multivalued dependency exists when there are at least three attributes (like X,Y and Z) in a relation and for a value of X there is a well defined set of values of Y and a well defined set of values of Z. However, the set of values of Y is independent of set Z and vice versa. Formal definition The formal definition is as follows: Let R be a relation and let \alpha \subseteq R and \beta \subseteq R be sets of attributes. The multivalued depend ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chase (algorithm)
The chase is a simple fixed-point algorithm testing and enforcing implication of data dependencies in database systems. It plays important roles in database theory as well as in practice. It is used, directly or indirectly, on an everyday basis by people who design databases, and it is used in commercial systems to reason about the consistency and correctness of a data design. New applications of the chase in meta-data management and data exchange are still being discovered. The chase has its origins in two seminal papers of 1979, one by Alfred V. Aho, Catriel Beeri, and Jeffrey D. Ullman and the other by David Maier, Alberto O. Mendelzon, and Yehoshua Sagiv. In its simplest application the chase is used for testing whether the projection of a relation schema constrained by some functional dependencies onto a given decomposition can be recovered by rejoining the projections. Let ''t'' be a tuple in \pi_(R) \bowtie \pi_(R) \bowtie ... \bowtie \pi_(R) where ''R'' is a relation a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Functional Dependency
In relational database theory, a functional dependency is a constraint between two sets of attributes in a relation from a database. In other words, a functional dependency is a constraint between two attributes in a relation. Given a relation ''R'' and sets of attributes X,Y \subseteq R, ''X'' is said to functionally determine ''Y'' (written ''X'' → ''Y'') if and only if each ''X'' value in ''R'' is associated with precisely one ''Y'' value in ''R''; ''R'' is then said to ''satisfy'' the functional dependency ''X'' → ''Y''. Equivalently, the projection \Pi_R is a function, i.e. ''Y'' is a function of ''X''. In simple words, if the values for the ''X'' attributes are known (say they are ''x''), then the values for the ''Y'' attributes corresponding to ''x'' can be determined by looking them up in ''any'' tuple of ''R'' containing ''x''. Customarily ''X'' is called the ''determinant'' set and ''Y'' the ''dependent'' set. A functional dependency FD: ''X'' → ''Y'' is called ''tr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Join Dependency
In database theory, a join dependency is a constraint on the set of legal relations over a database scheme. A table T is subject to a join dependency if T can always be recreated by joining multiple tables each having a subset of the attributes of T. If one of the tables in the join has all the attributes of the table T, the join dependency is called trivial. The join dependency plays an important role in the Fifth normal form, also known as ''project-join normal form'', because it can be proven that if a scheme R is decomposed in tables R_1 to R_n, the decomposition will be a lossless-join decomposition if the legal relations on R are restricted to a join dependency on R called *(R_1,R_2,\ldots,R_n). Another way to describe a join dependency is to say that the relationships in the join dependency are independent of each other. Unlike in the case of functional dependencies, there is no sound and complete axiomatization for join dependencies, though axiomatization exist for more e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tuple-generating Dependency
In relational database theory, a tuple-generating dependency (TGD) is a certain kind of constraint on a relational database. It is a subclass of the class of embedded dependencies (EDs). An algorithm known as the chase takes as input an instance that may or may not satisfy a set of TGDs (or more generally EDs) and, if it terminates (which is a priori undecidable), outputs an instance that does satisfy the TGDs. Definition A tuple-generating dependency is a sentence in first-order logic of the form: :\forall x_1,\ldots, x_n . \phi(x_1, \ldots, x_n) \rightarrow \exists y_1, \ldots, y_m, \psi(x_1, \ldots, x_n, y_1, \ldots, y_m) where \phi is a possibly empty and \psi is a non-empty conjunction of relational atoms. A relational atom has the form R(w_1, \ldots, w_h), where each of the terms w, \ldots, w_h are variables or constants. Fragments Several fragments of TGDs have been defined. For instance, ''full TGDs'' are TGDs which do not use the existential quantifier. Full TG ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equality-generating Dependency
In relational database theory, an equality-generating dependency (EGD) is a certain kind of constraint on data. It is a subclass of the class of embedded dependencies (ED). An algorithm known as the chase takes as input an instance that may or may not satisfy a set of EGDs (or, more generally, a set of EDs), and, if it terminates (which is a priori undecidable), output an instance that does satisfy the EGDs. An important subclass of equality-generating dependencies are functional dependencies. Definition An equality-generating dependency is a sentence in first-order logic of the form: :\forall x_1,\ldots,x_n . \phi(x_1,\ldots,x_n) \rightarrow \psi(y_1,\ldots,y_m) where \ \subseteq \, \phi is a conjunction of relational and equality atoms and \psi is a non-empty conjunction of equality atoms. A relational atom has the form R(w_1,\ldots,w_h) and an equality atom has the form w_i = w_j, where each of the terms w, ..., w_h, w_i, w_j are variables or constants. An equivalent de ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Embedded Dependency
In relational database theory, an embedded dependency (ED) is a certain kind of constraint on a relational database. It is the most general type of constraint used in practice, including both tuple-generating dependencies and equality-generating dependencies. Embedded dependencies can express functional dependencies, join dependencies, multivalued dependencies, inclusion dependencies, foreign key dependencies, and many more besides. An algorithm known as the chase takes as input an instance that may or may not satisfy a set of EDs, and, if it terminates (which is a priori undecidable), output an instance that does satisfy the EDs. Definition An embedded dependency (ED) is a sentence in first-order logic of the form: :\forall x_1,\ldots,x_n . \phi(x_1,\ldots,x_n) \rightarrow \exists z_1, \ldots, z_k . \psi(y_1,\ldots,y_m) Where \ = \ \setminus \ and \phi and \psi are conjunctions of relational and equality atoms. A relational atom has the form R(w_1,\ldots,w_h) and an equalit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inclusion Dependency
Referential integrity is a property of data stating that all its references are valid. In the context of relational databases, it requires that if a value of one attribute (column) of a relation (table) references a value of another attribute (either in the same or a different relation), then the referenced value must exist. For referential integrity to hold in a relational database, any column in a base table that is declared a foreign key can only contain either null values or values from a parent table's primary key or a candidate key. In other words, when a foreign key value is used it must reference a valid, existing primary key in the parent table. For instance, deleting a record that contains a value referred to by a foreign key in another table would break referential integrity. Some relational database management systems (RDBMS) can enforce referential integrity, normally either by deleting the foreign key rows as well to maintain integrity, or by returning an error and n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Full Typed Dependency
Full may refer to: * People with the surname Full, including: ** Mr. Full (given name unknown), acting Governor of German Cameroon, 1913 to 1914 * A property in the mathematical field of topology; see Full set * A property of functors in the mathematical field of category theory; see Full and faithful functors * Satiety, the absence of hunger * A standard bed size, see Bed * Fulling, also known as tucking or walking ("waulking" in Scotland), term for a step in woollen clothmaking (verb: ''to full'') * Full-Reuenthal, a municipality in the district of Zurzach in the canton of Aargau in Switzerland See also *"Fullest", a song by the rapper Cupcakke Elizabeth Eden Harris (born May 31, 1997), known professionally as Cupcakke (often stylized as CupcakKe; pronounced ), is an American rapper from Chicago, Illinois. She is known for her hypersexualised, brazen, and often comical persona and mus ... * Ful (other) {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
