Database Management Systems Solutions Manual Third Edition
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Tuple Relational Calculus Formula Defines Relation
COS 425: Database and Information Management Systems Relational model: Relational calculus Tuple Relational Calculus Queries are formulae, which define sets using: 1. Constants 2. Predicates (like select of algebra ) 3. BooleanE and, or, not 4.A there exists 5. for all • Variables range over tuples • Attributes of a tuple T can be referred to in predicates using T.attribute_name Example: { T | T ε tp and T.rank > 100 } |__formula, T free ______| tp: (name, rank); base relation of database Formula defines relation • Free variables in a formula take on the values of tuples •A tuple is in the defined relation if and only if when substituted for a free variable, it satisfies (makes true) the formula Free variable: A E x, x bind x – truth or falsehood no longer depends on a specific value of x If x is not bound it is free 1 Quantifiers There exists: E x (f(x)) for formula f with free variable x • Is true if there is some tuple which when substituted for x makes f true For all: A x (f(x)) for formula f with free variable x • Is true if any tuple substituted for x makes f true i.e. all tuples when substituted for x make f true Example E {T | E A B (A ε tp and B ε tp and A.name = T.name and A.rank = T.rank and B.rank =T.rank and T.name2= B.name ) } • T not constrained to be element of a named relation • T has attributes defined by naming them in the formula: T.name, T.rank, T.name2 – so schema for T is (name, rank, name2) unordered • Tuples T in result have values for (name, rank, name2) that satisfy the formula • What is the resulting relation? Formal definition: formula • A tuple relational calculus formula is – An atomic formula (uses predicate and constants): •T ε R where – T is a variable ranging over tuples – R is a named relation in the database – a base relation •T.a op W.b where – a and b are names of attributes of T and W, respectively, – op is one of < > = ≠≤≥ •T.a op constant • constant op T.a 2 Formal definition: formula cont. -
Relational Algebra
Relational Algebra Instructor: Shel Finkelstein Reference: A First Course in Database Systems, 3rd edition, Chapter 2.4 – 2.6, plus Query Execution Plans Important Notices • Midterm with Answers has been posted on Piazza. – Midterm will be/was reviewed briefly in class on Wednesday, Nov 8. – Grades were posted on Canvas on Monday, Nov 13. • Median was 83; no curve. – Exam will be returned in class on Nov 13 and Nov 15. • Please send email if you want “cheat sheet” back. • Lab3 assignment was posted on Sunday, Nov 5, and is due by Sunday, Nov 19, 11:59pm. – Lab3 has lots of parts (some hard), and is worth 13 points. – Please attend Labs to get help with Lab3. What is a Data Model? • A data model is a mathematical formalism that consists of three parts: 1. A notation for describing and representing data (structure of the data) 2. A set of operations for manipulating data. 3. A set of constraints on the data. • What is the associated query language for the relational data model? Two Query Languages • Codd proposed two different query languages for the relational data model. – Relational Algebra • Queries are expressed as a sequence of operations on relations. • Procedural language. – Relational Calculus • Queries are expressed as formulas of first-order logic. • Declarative language. • Codd’s Theorem: The Relational Algebra query language has the same expressive power as the Relational Calculus query language. Procedural vs. Declarative Languages • Procedural program – The program is specified as a sequence of operations to obtain the desired the outcome. I.e., how the outcome is to be obtained. -
Tuple Relational Calculus Formula Defines Relation Quantifiers Example
COS 597A: Tuple Relational Calculus Principles of Queries are formulae, which define sets using: Database and Information Systems 1. Constants 2. Predicates (like select of algebra ) 3. Boolean and, or, not Relational model: 4. ∃ there exists 5. ∀ for all Relational calculus Variables range over tuples Value of an attribute of a tuple T can be referred to in predicates using T[attribute_name] Example: { T | T ε Winners and T[year] > 2006 } |__formula, T free ______| Winners: (name, tournament, year); base relation of database Formula defines relation Quantifiers • Free variables in a formula take on the values of There exists: ∃x (f(x)) for formula f with free tuples variable x • A tuple is in the defined relation if and only if • Is true if there is some tuple which when substituted when substituted for a free variable, it satisfies for x makes f true (makes true) the formula For all: ∀x (f(x)) for formula f with free variable x Free variable: • Is true if any tuple substituted for x makes f true i.e. all tuples when substituted for x make f true ∃x, ∀x bind x – truth or falsehood no longer depends on a specific value of x If x is not bound it is free Example Formal definition: formula • A tuple relational calculus formula is {T |∃A ∃B (A ε Winners and B ε Winners and – An atomic formula (uses predicate and constants): A[name] = T[name] and A[tournament] = T[tournament] and • T ε R where B[tournament] =T[tournament] and T[name2] = B[name] ) } – T is a variable ranging over tuples – R is a named relation in the database – a base relation • T not constrained to be element of a named relation • T[a] op W[b] where • Result has attributes defined by naming them in the formula: – a and b are names of attributes of T and W, respectively, T[name], T[tournament], T[name2] – op is one of < > = ≠ ≤ ≥ – so schema for result: (name, tournament, name2) • T[a] op constant unordered • constant op T[a] • Tuples T in result have values for (name, tournament, name2) that satisfy the formula • What is the resulting relation? 1 Formal definition: formula cont. -
Relational Algebra and SQL Relational Query Languages
Relational Algebra and SQL Chapter 5 1 Relational Query Languages • Languages for describing queries on a relational database • Structured Query Language (SQL) – Predominant application-level query language – Declarative • Relational Algebra – Intermediate language used within DBMS – Procedural 2 1 What is an Algebra? · A language based on operators and a domain of values · Operators map values taken from the domain into other domain values · Hence, an expression involving operators and arguments produces a value in the domain · When the domain is a set of all relations (and the operators are as described later), we get the relational algebra · We refer to the expression as a query and the value produced as the query result 3 Relational Algebra · Domain: set of relations · Basic operators: select, project, union, set difference, Cartesian product · Derived operators: set intersection, division, join · Procedural: Relational expression specifies query by describing an algorithm (the sequence in which operators are applied) for determining the result of an expression 4 2 The Role of Relational Algebra in a DBMS 5 Select Operator • Produce table containing subset of rows of argument table satisfying condition σ condition (relation) • Example: σ Person Hobby=‘stamps’(Person) Id Name Address Hobby Id Name Address Hobby 1123 John 123 Main stamps 1123 John 123 Main stamps 1123 John 123 Main coins 9876 Bart 5 Pine St stamps 5556 Mary 7 Lake Dr hiking 9876 Bart 5 Pine St stamps 6 3 Selection Condition • Operators: <, ≤, ≥, >, =, ≠ • Simple selection -
Regulations & Syllabi for AMIETE Examination (Computer Science
Regulations & Syllabi For AMIETE Examination (Computer Science & Engineering) Published under the authority of the Governing Council of The Institution of Electronics and Telecommunication Engineers 2, Institutional Area, Lodi Road, New Delhi – 110 003 (India) (2013 Edition) Website : http://www.iete.org Toll Free No : 18001025488 Tel. : (011) 43538800-99 Fax : (011) 24649429 Email : [email protected] [email protected] Prospectus Containing Regulations & Syllabi For AMIETE Examination (Computer Science & Engineering) Published under the authority of the Governing Council of The Institution of Electronics and Telecommunication Engineers 2, Institutional Area, Lodi Road, New Delhi – 110 003 (India) (2013 Edition) Website : http://www.iete.org Toll Free No : 18001025488 Tel. : (011) 43538800-99 Fax : (011) 24649429 Email : [email protected] [email protected] CONTENTS 1. ABOUT THE INSTITUTION 1 2. ELIGIBILITY 4 3. ENROLMENT 5 4. AMIETE EXAMINATION 6 5. ELIGIBILITY FOR VARIOUS SUBJECTS 6 6. EXEMPTIONS 7 7. CGPA SYSTEM 8 8. EXAMINATION APPLICATION 8 9. EXAMINATION FEE 9 10. LAST DATE FOR RECEIPT OF EXAMINATION APPLICATION 9 11. EXAMINATION CENTRES 10 12. USE OF UNFAIR MEANS 10 13. RECOUNTING 11 14. IMPROVEMENT OF GRADES 11 15. COURSE CURRICULUM (Computer Science) (CS) (Appendix-‘A’) 13 16. OUTLINE SYLLABUS (CS) (Appendix-‘B’) 16 17. COURSE CURRICULUM (Information Technology) (IT) (Appendix-‘C”) 24 18. OUTLINE SYLLABUS (IT) (Appendix-‘D’) 27 19. COURSE CURRICULUM (Electronics & Telecommunication) (ET) 35 (Appendix-‘E’) 20. OUTLINE SYLLABUS (ET) (Appendix-‘F’) 38 21. DETAILED SYLLABUS (CS) (Appendix-’G’) 45 22. RECOGNITIONS GRANTED TO THE AMIETE EXAMINATION BY STATE 113 GOVERNMENTS / UNIVERSITIES / INSTITUTIONS (Appendix-‘I’) 23. RECOGNITIONS GRANTED TO THE AMIETE EXAMINATION BY 117 GOVERNMENT OF INDIA / OTHER AUTHORITIES ( Annexure I - V) 24. -
Session 5 – Main Theme
Database Systems Session 5 – Main Theme Relational Algebra, Relational Calculus, and SQL Dr. Jean-Claude Franchitti New York University Computer Science Department Courant Institute of Mathematical Sciences Presentation material partially based on textbook slides Fundamentals of Database Systems (6th Edition) by Ramez Elmasri and Shamkant Navathe Slides copyright © 2011 and on slides produced by Zvi Kedem copyight © 2014 1 Agenda 1 Session Overview 2 Relational Algebra and Relational Calculus 3 Relational Algebra Using SQL Syntax 5 Summary and Conclusion 2 Session Agenda . Session Overview . Relational Algebra and Relational Calculus . Relational Algebra Using SQL Syntax . Summary & Conclusion 3 What is the class about? . Course description and syllabus: » http://www.nyu.edu/classes/jcf/CSCI-GA.2433-001 » http://cs.nyu.edu/courses/fall11/CSCI-GA.2433-001/ . Textbooks: » Fundamentals of Database Systems (6th Edition) Ramez Elmasri and Shamkant Navathe Addition Wesley ISBN-10: 0-1360-8620-9, ISBN-13: 978-0136086208 6th Edition (04/10) 4 Icons / Metaphors Information Common Realization Knowledge/Competency Pattern Governance Alignment Solution Approach 55 Agenda 1 Session Overview 2 Relational Algebra and Relational Calculus 3 Relational Algebra Using SQL Syntax 5 Summary and Conclusion 6 Agenda . Unary Relational Operations: SELECT and PROJECT . Relational Algebra Operations from Set Theory . Binary Relational Operations: JOIN and DIVISION . Additional Relational Operations . Examples of Queries in Relational Algebra . The Tuple Relational Calculus . The Domain Relational Calculus 7 The Relational Algebra and Relational Calculus . Relational algebra . Basic set of operations for the relational model . Relational algebra expression . Sequence of relational algebra operations . Relational calculus . Higher-level declarative language for specifying relational queries 8 Unary Relational Operations: SELECT and PROJECT (1/3) . -
Ch06-The Relational Algebra and Calculus.Pdf
Copyright © 2007 Ramez Elmasri and Shamkant B. Navathe Slide 6- 1 Chapter 6 The Relational Algebra and Calculus Copyright © 2007 Ramez Elmasri and Shamkant B. Navathe Chapter Outline Relational Algebra Unary Relational Operations Relational Algebra Operations From Set Theory Binary Relational Operations Additional Relational Operations Examples of Queries in Relational Algebra Relational Calculus Tuple Relational Calculus Domain Relational Calculus Example Database Application (COMPANY) Overview of the QBE language (appendix D) Copyright © 2007 Ramez Elmasri and Shamkant B. Navathe Slide 6- 3 Relational Algebra Overview Relational algebra is the basic set of operations for the relational model These operations enable a user to specify basic retrieval requests (or queries) The result of an operation is a new relation, which may have been formed from one or more input relations This property makes the algebra “closed” (all objects in relational algebra are relations) Copyright © 2007 Ramez Elmasri and Shamkant B. Navathe Slide 6- 4 Relational Algebra Overview (continued) The algebra operations thus produce new relations These can be further manipulated using operations of the same algebra A sequence of relational algebra operations forms a relational algebra expression The result of a relational algebra expression is also a relation that represents the result of a database query (or retrieval request) Copyright © 2007 Ramez Elmasri and Shamkant B. Navathe Slide 6- 5 Brief History of Origins of Algebra Muhammad ibn Musa al-Khwarizmi (800-847 CE) wrote a book titled al-jabr about arithmetic of variables Book was translated into Latin. Its title (al-jabr) gave Algebra its name. Al-Khwarizmi called variables “shay” “Shay” is Arabic for “thing”. -
Relational Algebra & Relational Calculus
Relational Algebra & Relational Calculus Lecture 4 Kathleen Durant Northeastern University 1 Relational Query Languages • Query languages: Allow manipulation and retrieval of data from a database. • Relational model supports simple, powerful QLs: • Strong formal foundation based on logic. • Allows for optimization. • Query Languages != programming languages • QLs not expected to be “Turing complete”. • QLs not intended to be used for complex calculations. • QLs support easy, efficient access to large data sets. 2 Relational Query Languages • Two mathematical Query Languages form the basis for “real” query languages (e.g. SQL), and for implementation: • Relational Algebra: More operational, very useful for representing execution plans. • Basis for SEQUEL • Relational Calculus: Let’s users describe WHAT they want, rather than HOW to compute it. (Non-operational, declarative.) • Basis for QUEL 3 4 Cartesian Product Example • A = {small, medium, large} • B = {shirt, pants} A X B Shirt Pants Small (Small, Shirt) (Small, Pants) Medium (Medium, Shirt) (Medium, Pants) Large (Large, Shirt) (Large, Pants) • A x B = {(small, shirt), (small, pants), (medium, shirt), (medium, pants), (large, shirt), (large, pants)} • Set notation 5 Example: Cartesian Product • What is the Cartesian Product of AxB ? • A = {perl, ruby, java} • B = {necklace, ring, bracelet} • What is BxA? A x B Necklace Ring Bracelet Perl (Perl,Necklace) (Perl, Ring) (Perl,Bracelet) Ruby (Ruby, Necklace) (Ruby,Ring) (Ruby,Bracelet) Java (Java, Necklace) (Java, Ring) (Java, Bracelet) 6 Mathematical Foundations: Relations • The domain of a variable is the set of its possible values • A relation on a set of variables is a subset of the Cartesian product of the domains of the variables. • Example: let x and y be variables that both have the set of non- negative integers as their domain • {(2,5),(3,10),(13,2),(6,10)} is one relation on (x, y) • A table is a subset of the Cartesian product of the domains of the attributes. -
Relational Algebra Expression Evaluation
Faculty of Informatics, Masaryk University Relational Algebra Expression Evaluation Bachelor's Thesis Lucie Molkov´a Brno, spring 2009 Declaration Thereby I declare that this thesis is my original work, which I have created on my own. All sources and literature used in writing the thesis, as well as any quoted material, are properly cited, including full reference to its source. Advisor: RNDr. Vlastislav Dohnal, Ph.D. Acknowledgements I would like to thank my advisor RNDr. Vlastislav Dohnal, Ph.D. for the help and motivation he provided throughout my work on this thesis and to Loren K. Rhodes, Ph.D. for valuable inputs. Special thanks go to Tom´aˇsJanouˇsekand Bc. Petr Roˇckai for support and ideas that saved me a lot of time. Abstract Relational algebra is a query language that is being used to explain basic relational operations and their principles. Many books and articles are concerned with the theory of relational algebra, however there is no practical use for it. One of the reasons is that no software exists that would allow a real use of relational alge- bra. Most of the currently used relational database management systems work with SQL queries. This work therefore describes and implemets a tool that transforms a relational algebra expressions into SQL queries, allowing the expressions to be evaluated in standard databases. This work also defines a new, applicable syntax for relational algebra and describes its grammar in order to ensure the correctness of the expressions. Keywords Relationa Algebra, SQL, Transformation, Perl, Parsing, Parse::Yapp, Syntax Anal- ysis, Semantic Analysis Contents 1 Introduction 7 1.1 Objectives . -
Algebraic Operations on Tabular Data Context 6.1 Basic Idea of Relational
Context Database Design: 6 The Relational Data Model: e s - developing a relational a Requirements analysis b database schema Algebraic operations on tabular data a t Design: a d - formal theory 6.1 Basic idea of relational languages Conceptual Design g n i Data handling in a rela- s 6.2 Relational Algebra operations u tional database Schema design d 6.3 Relational Algebra: Syntax and Semantics n - Algebra,-calculus -SQL -logical a (“create tables”) g Extensions 6.4. More Operators n i n g Using Databases 6.5 Special Topics of RA i s from application progs 6.5.1 Relational algebra operators in SQL e D : Special topics, 6.5.2 Relational completeness 1 Schema design t Physical Schema, 6.5.3 What is missing in RA? r a -physical P 6.5.4 RA operator trees Part 2: (“create access path”) Implementation of DBS Loading, administration, Transaction, Kemper / Eickler: 3.4, Elmasri /Navathe: chap. 74-7.6, tuning, maintenance, Concurrency control Garcia-Molina, Ullman, Widom: chap. 5 reorganization Recovery 6.1 Basic idea of relational languages Relational Languages • Data Model: Important concepts Goal of language design Language for definition and Given a relational database like the Video shop DB handling (manipulation ) of data Design a language, which allows to express queries – Languages for handling data: like: • Relational Algebra (RA) as a semantically well defined - Customers who rented videos for more than 100 $ last month applicative language - List of all movies no copy of which have been on loan since 2 month - List the total sales volume of each movie within the last year • Relational tuple calculus (domain calculus): predicate logic - Is there anybody whose rented movies all have category "horror"? interpretation of data and queries y? ……. -
RELATIONAL DATABASE PRINCIPLES © Donald Ravey 2008
RELATIONAL DATABASE PRINCIPLES © Donald Ravey 2008 DATABASE DEFINITION In a loose sense, almost anything that stores data can be called a database. So a spreadsheet, or a simple text file, or the cards in a Rolodex, or even a handwritten list, can be called a database. However, we are concerned here with computer software that manages the addition, modification, deletion and retrieval of data from specially formatted computer files. Such software is often called a Relational Database Management System (RDBMS) and that will be the subject of the remainder of this tutorial. RELATIONAL DATABASE HISTORY The structure of a relational database is quite specific. Data is contained in one or more tables (the purists call them relations). A table consists of rows (also known as tuples or records), each of which contains columns (also called attributes or fields). Within any one table, all rows must contain the same columns; that is, every table has a uniform structure; if any row contains a Zipcode column, every row will contain a Zipcode column. In the late 1960’s, a mathematician and computer scientist at IBM, Dr. E. F. (Ted) Codd, developed the principles of what we now call relational databases, based on mathematical set theory. He constructed a consistent logical framework and a sort of calculus that would insure the integrity of stored data. In other words, he effectively said, If you structure data in accordance with these rules, and if you operate on the data within these constraints, your data will be guaranteed to remain consistent and certain operations will always work. -
Relational Databases, Logic, and Complexity
Relational Databases, Logic, and Complexity Phokion G. Kolaitis University of California, Santa Cruz & IBM Research-Almaden [email protected] 2009 GII Doctoral School on Advances in Databases 1 What this course is about Goals: Cover a coherent body of basic material in the foundations of relational databases Prepare students for further study and research in relational database systems Overview of Topics: Database query languages: expressive power and complexity Relational Algebra and Relational Calculus Conjunctive queries and homomorphisms Recursive queries and Datalog Selected additional topics: Bag Semantics, Inconsistent Databases Unifying Theme: The interplay between databases, logic, and computational complexity 2 Relational Databases: A Very Brief History The history of relational databases is the history of a scientific and technological revolution. Edgar F. Codd, 1923-2003 The scientific revolution started in 1970 by Edgar (Ted) F. Codd at the IBM San Jose Research Laboratory (now the IBM Almaden Research Center) Codd introduced the relational data model and two database query languages: relational algebra and relational calculus . “A relational model for data for large shared data banks”, CACM, 1970. “Relational completeness of data base sublanguages”, in: Database Systems, ed. by R. Rustin, 1972. 3 Relational Databases: A Very Brief History Researchers at the IBM San Jose Laboratory embark on the System R project, the first implementation of a relational database management system (RDBMS) In 1974-1975, they develop SEQUEL , a query language that eventually became the industry standard SQL . System R evolved to DB2 – released first in 1983. M. Stonebraker and E. Wong embark on the development of the Ingres RDBMS at UC Berkeley in 1973.