|
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 Some recognized dependency types are: * Functional dependency * Join dependency * Multivalued dependency * Tuple-generating dependency * Transitive dependency Transitivity or transitive may refer to: Grammar * Transitivity (grammar), a property regarding whether a lexical item denotes a transitive object * Transitive verb, a verb which takes an object * Transitive case, a grammatical case to mark ar ... * Equality-generating dependency * Embedded dependency * Inclusion dependency * Fu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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 theory, computational complexity and expressive power (computer science), expressive power of queries, finite model theory, database design theory, dependency theory (database theory), dependency theory, foundations of concurrency control and database recovery, deductive databases, temporal database, 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Database
In computing, a database is an organized collection of data or a type of data store based on the use of a database management system (DBMS), the software that interacts with end users, applications, and the database itself to capture and analyze the data. The DBMS additionally encompasses the core facilities provided to administer the database. The sum total of the database, the DBMS and the associated applications can be referred to as a database system. Often the term "database" is also used loosely to refer to any of the DBMS, the database system or an application associated with the database. Before digital storage and retrieval of data have become widespread, index cards were used for data storage in a wide range of applications and environments: in the home to record and store recipes, shopping lists, contact information and other organizational data; in business to record presentation notes, project research and notes, and contact information; in schools as flash c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Functional Dependency
In relational database theory, a functional dependency is the following constraint between two attribute sets in a relation: Given a relation ''R'' and attribute sets ''X'',''Y'' \subseteq ''R'', ''X'' is said to functionally determine ''Y'' (written ''X'' → ''Y'') if each ''X'' value is associated with precisely one ''Y'' value. ''R'' is then said to satisfy the functional dependency ''X'' → ''Y''. Equivalently, the projection \Pi_R is a function, that is, ''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 ''trivial'' if ''Y'' is a subset of ''X''. In other words, a dependency FD: ''X'' → ''Y'' means that the values of ''Y'' ar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Candidate Key
A candidate key, or simply a key, of a relational database is any set of columns that have a unique combination of values in each row, with the additional constraint that removing any column could produce duplicate combinations of values. A candidate key is a minimal superkey, i.e., a superkey that does not contain a smaller one. Therefore, a relation can have multiple candidate keys, each with a different number of attributes. 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 is not minimal, some subset of that will be minimal. There is a functional dependency from the candidate key to all the attributes in the relatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Relational Algebra
In database theory, relational algebra is a theory that uses algebraic structures for modeling data and defining queries on it with well founded semantics (computer science), semantics. The theory was introduced by Edgar F. Codd. The main application of relational algebra is to provide a theoretical foundation for relational databases, particularly query languages for such databases, chief among which is SQL. Relational databases store tabular data represented as relation (database), relations. Queries over relational databases often likewise return tabular data represented as relations. The main purpose of relational algebra is to define Operator (mathematics), operators that transform one or more input relations to an output relation. Given that these operators accept relations as input and produce relations as output, they can be combined and used to express complex queries that transform multiple input relations (whose data are stored in the database) into a single output rela ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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 schema and let \alpha \subseteq R and \beta \subseteq R be sets of attributes. The multivalue ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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 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 q ... 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 th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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 (5NF), 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 f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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 schema and let \alpha \subseteq R and \beta \subseteq R be sets of attributes. The multivalue ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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 TGDs ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Transitive Dependency
Transitivity or transitive may refer to: Grammar * Transitivity (grammar), a property regarding whether a lexical item denotes a transitive object * Transitive verb, a verb which takes an object * Transitive case, a grammatical case to mark arguments of a transitive verb Logic and mathematics * Transitive group action * Transitive relation, a binary relation in which if ''A'' is related to ''B'' and ''B'' is related to ''C'', then ''A'' is related to ''C'' * Syllogism, a related notion in propositional logic * Intransitivity, properties of binary relations in mathematics * Arc-transitive graph, a graph whose automorphism group acts transitively upon ordered pairs of adjacent vertices * Edge-transitive graph, a graph whose automorphism group acts transitively upon its edges * Vertex-transitive graph, a graph whose automorphism group acts transitively upon its vertices * Transitive set a set ''A'' such that whenever ''x'' ∈ ''A'', and ''y'' ∈ ''x'', then ''y'' ∈ ''A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
