'Relation r' presentation slideshows

Schema Design & Refinement (cont.)

Schema Design & Refinement (cont.). Lecture #7. What We Covered Last Time. Functional Dependencies and Keys. Functional Dependencies. A form of constraint (hence, part of the schema) Finding them is part of the database design Used heavily in schema refinement. Definition:

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Partial Order Relations

Partial Order Relations. Lecture 50 Section 10.5 Wed, Apr 20, 2005. Antisymmetry. A relation R on a set A is antisymmetric if for all a , b ? A , ( a , b ) ? R and ( b , a ) ? R ? a = b . This is equivalent to ( a , b ) ? R and a ? b ? ( b , a ) ? R .

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Lecture 3 Functional Dependency and Normal Forms

CS157B. Lecture 3 Functional Dependency and Normal Forms. Prof. Sin-Min Lee Department of Computer Science. Database Design Process. Application 1. Application 2. Application 3. Application 4. External Model. External Model. External Model. External Model. Application 1.

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Schema Refinement and Normal Forms

Schema Refinement and Normal Forms. Chapter 19. The Evils of Redundancy. Redundancy is at the root of several problems associated with relational schemas: redundant storage, insert/delete/update anomalies Main refinement technique: decomposition

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CS201: Data Structures and Discrete Mathematics I

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Chapter 8: Relational Database Design

Chapter 8: Relational Database Design. First Normal Form Functional Dependencies Decomposition Boyce-Codd Normal Form Third Normal Form. First Normal Form. R is in first normal form if the domains of all attributes of R are atomic

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Relations

Relations. Rosen 5 th ed., ch. 7. Relations. Relationships between elements of sets occur very often. (Employee, Salary) (Students, Courses, GPA) We use ordered pairs (or n-tuples ) of elements from the sets to represent relationships. . Binary Relations.

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Relational Algebra & Client-Server Systems, CS263 Lectures 11 and 12

Relational Algebra & Client-Server Systems, CS263 Lectures 11 and 12. Relational Algebra. Relational algebra operations work on one or more relations to define another relation leaving the original intact.

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Decomposition, 3NF, BCNF

Decomposition, 3NF, BCNF. Souhad M. Daraghma. Decomposition of a Relation Schema. If a relation is not in a desired normal form, it can be decomposed into multiple relations that each are in that normal form.

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Chapter 7: Relational Database Design

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Chapter 8: Relational Database Design

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Logical Query Languages

Logical Query Languages. Motivation: Logical rules extend more naturally to recursive queries than does relational algebra. Used in SQL recursion. Logical rules form the basis for many information-integration systems and applications. Datalog Example. Likes( drinker , beer )

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Schedule

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SQL and Relational Algebra

SQL and Relational Algebra. Zaki Malik September 02, 2008. Basics of Relational Algebra. Four types of operators: Select/Show parts of a single relation: projection and selection. Usual set operations (union, intersection, difference).

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Preliminaries

Preliminaries . Language: Set of Strings. Specification and recognition of languages Sets Operations Defining sets ( inductively ) Proving properties about sets ( using induction ) Defining functions on sets ( using recursion ) Proving properties about functions ( using induction )

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Discrete Mathematics Relations

Discrete Mathematics Relations. What is a relation. Relation generalizes the notion of functions. Recall: A function takes EACH element from a set and maps it to a UNIQUE element in another set f: X ? Y ? x ? X, ? y such that f(x) = y Let A and B be sets.

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Suppose the relation R ? A ? B is a function

Inverse function . . Suppose the relation R ? A ? B is a function. It means that for any a ? A there exists a unique b ? B, ( a , b ) ? R , or we have f ( a )= b. . Then the inverse relation R -1 = { ( b , a ) | b ? B , a ? A and f ( a )= b } ? B ? A .

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Algorithmic Software Verification

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Partial Orders

Partial Orders. Definitions. A relation R on set A is a partial order if it is: reflexive antisymmetric transitive. A is called a partially ordered set or poset . [A;R] means A is partially ordered by R. Example: [ P({1,2}); ? ] ( draw its digraph ). Definitions .

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