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First Normal Form (1NF) is a property of a relational database table that requires each column to contain atomic values and each entry in a column to be of the same data type. Achieving 1NF helps eliminate duplicate data and ensures that the database structure is efficient and logically organized.
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Second Normal Form (2NF) is a stage in the normalization process of a relational database where a table is in First Normal Form and all non-key attributes are fully functionally dependent on the primary key. This ensures that there are no partial dependencies of any column on the primary key, thereby reducing redundancy and improving data integrity.
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Third Normal Form (3NF) is a database normalization stage that ensures no transitive dependencies exist, meaning non-key attributes are not dependent on other non-key attributes. This form enhances data integrity and reduces redundancy by ensuring that each non-key attribute is only dependent on the primary key.
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Boyce-Codd Normal Form (BCNF) is a database normalization form used to eliminate redundancy and ensure data integrity by requiring that every determinant in a relation is a candidate key. It is a stricter version of the Third Normal Form (3NF), addressing anomalies that 3NF may not handle by ensuring that no non-trivial functional dependencies exist unless they are on superkeys.
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Fourth Normal Form (4NF) is a level of database normalization designed to reduce redundancy by ensuring that multi-valued dependencies are eliminated. It builds on the principles of Third Normal Form by addressing situations where a record contains two or more independent multi-valued facts about an entity, ensuring that these facts are stored in separate tables.
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Fifth Normal Form (5NF), also known as Project-Join Normal Form (PJNF), is the highest level of database normalization aimed at eliminating redundancy in relational databases by ensuring that every join dependency in the database is a consequence of the candidate keys. It is particularly useful in complex databases where data is decomposed into smaller tables without losing any information or introducing redundancy, ensuring data integrity and consistency.
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Functional dependency is a constraint between two sets of attributes in a relational database, where one set uniquely determines another. It is fundamental to database normalization, ensuring data integrity and reducing redundancy by organizing data efficiently.
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Transitive dependency in database normalization occurs when a non-prime attribute is functionally dependent on another non-prime attribute, which in turn depends on a primary key. This type of dependency can lead to redundancy and anomalies, and is typically resolved by normalizing the database to Third Normal Form (3NF).
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Data redundancy occurs when the same piece of data is stored in multiple places within a database or data storage system, which can lead to inconsistencies and increased storage costs. While sometimes intentional for backup and performance reasons, excessive redundancy can complicate data management and compromise data integrity.
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Database normalization is a process used to organize a database into tables and columns to reduce data redundancy and improve data integrity. It involves dividing large tables into smaller, related tables and defining relationships between them to ensure data dependencies make sense and are logical.
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Proof normalization is a process in formal logic and type theory that transforms a proof into a normal form, often simplifying it by eliminating detours and redundancies. This process is crucial for proving consistency, decidability, and other meta-theoretical properties of logical systems and programming languages.
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Strong normalization is a property of a rewriting system, indicating that every sequence of rewrites eventually leads to a normal form, where no further rewrites are possible. This ensures termination of computations in systems like lambda calculus, making it a critical aspect of proving program correctness and consistency in formal systems.
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A Garside element is a specific type of element in a braid group that facilitates the solution of the word and Conjugacy Problems by allowing for the construction of a lattice structure on the group. It is crucial in the study of braid groups as it provides a means to understand the algebraic and geometric properties of these groups through the use of normal forms and orderings.
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Rewriting systems are formal frameworks used to define and implement transformations on abstract structures, such as strings, trees, or graphs, by applying a set of rules. They are fundamental in computer science for tasks like automated theorem proving, program transformation, and symbolic computation.
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Canonical form refers to a standard or simplified representation of a mathematical object or expression, which allows for easier comparison and manipulation. It is widely used in various fields such as linear algebra, logic, and computer science to achieve consistency and efficiency in problem-solving and communication.
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