article

Free access

Decompositions and functional dependencies in relations

Authors:

W. W. Armstrong,

C. DeobelAuthors Info & Claims

ACM Transactions on Database Systems (TODS), Volume 5, Issue 4

Pages 404 - 430

https://doi.org/10.1145/320610.320620

Published: 01 December 1980 Publication History

Abstract

A general study is made of two basic integrity constraints on relations: functional and multivalued dependencies. The latter are studied via an equivalent concept: decompositions. A model is constructed for any possible combination of functional dependencies and decompositions. The model embodies some decompositions as unions of relations having different schemata of functional dependencies. This suggests a new, stronger integrity constraint, the degenerate decomposition. More generally, the theory demonstrates the importance of using the union operation in database design and of allowing different schemata on the operands of a union. Techniques based on the union lead to a method for solving the problem of membership of a decomposition in the closure of a given set of functional dependencies and decompositions. The concept of antiroot is introduced as a tool for describing families of decompositions, and its fundamental importance for database design is indicated.

References

[1]

ARMSTRONG, W.W. Dependency structures of database relationships, In Proc. IFIP 74, North- Holland Pub. Co., Amsterdam, 1974, pp. 580-583.

[2]

BEERI, C. Unpublished manuscript.

[3]

BEERI, C., FAGIN, R., AND HOWARD, J.H. A complete axiomatization for functional and multivalued dependencies in database relations. In Proc. ACM SIGMOD Int. Conf. Management of Data, Toronto, 1977, pp. 47-61.

Digital Library

[4]

B~RNSTEIS, P.A. Synthesizing third normal form relations from functional dependencies. ACM Trans. Database Syst. 1, 4 (Dec. 1976), 277-298.

Digital Library

[5]

BERNSTEIN, P.A., AND BEERI, C. An algorithmic approach to normalization of relational database schemas. TR CSRG-73, Computer Systems Research Group, Univ. Toronto, Sept. 1976.

[6]

CObb, E.F. Recent investigations in relational database systems. In Proc. IFIP 74, North- Holland Pub. Co., Amsterdam, 1974, pp. 1017-1021.

[7]

CODD, E.F. Further normalization of the data base relational model. In Data Base Systems, Courant Institute Computer Science Symposia Series 6. Prentice-Hall, Englewood Cliffs, N.J., 1971, pp. 33-64.

[8]

DATE, C.J. An Introduction to Database Systems, 2nd ed. Addison-Wesley, Reading, Mass., 1977.

Digital Library

[9]

DELOBEL, C. Normalization and hierarchical dependencies in the relational data model. ACM Trans. Database Syst. 3, 3 (Sept. I978), 201-222.

Digital Library

[10]

DELOBEL, C., AND CASEY, R.G. Decomposition of a data base and the theory of Boolean switching functions. IBM J. Res. and Develop. 17, 5 (Sept. 1973), 374-386.

Digital Library

[11]

DZLOB~.L, C., AND PARKER, D.S. Functional and multivalued dependencies in a relational database and the theory of Boolean switching functions. Rapport de Recherche no. 142, Laboratoire d'informatique et de mathdmatiques appliqu~es de Grenoble, Nov. 1978.

[12]

FAGIN, R. Multivalued dependencies and a new normal form for relational databases. A CM Trans. Database Syst. 2, 3 {Sept. 1977), 262-278.

Digital Library

[13]

MZRRETT, T.H. Multidimensional paging for efficient data base querying. In Proc. Int. Conf. Data Base Management Systems (ICMOD 78), Milano, June 1978, pp. 277-290.

[14]

PAREDAENS, J. The interaction of integrity constraints in an information system. Rep. R-372, M.B.L.E. Research Labs., Brussels, 1978.

[15]

SAGIV, Y., AND FAGIN, R. An equivalence between relational database dependencies and a subclass of propositional logic. IBM Res. Rep. RJ 2500 {32750), March 1979. (References 11 and 15 have been combined into one paper: SAGIV, Y., DELOBEL, C., PARKER, D.S., AND FAGIN, R. An equivalence between relational database dependencies and a subclass of propositional logic. To appear in J. ACM.)

[16]

SMITH, J.M., AND SMITH, D.C.P. Database abstractions: Aggregation and generalization. ACM Trans. Database Syst. 2, 2 (June 1977), 105-133.

Digital Library

[17]

ZANIOLO, C., AND MELKANOFF, M.A. On the design of relational database schemas. To appear in A CM Trans. Database Syst.

Digital Library

Cited By

Suciu D(2023)Applications of Information Inequalities to Database Theory Problems2023 38th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)10.1109/LICS56636.2023.10175769(1-30)Online publication date: 26-Jun-2023
https://doi.org/10.1109/LICS56636.2023.10175769
Kwashie SLiu LLiu JStumptner MLi JYang L(2019)CertusProceedings of the VLDB Endowment10.14778/3311880.331188312:6(653-666)Online publication date: 1-Feb-2019
https://dl.acm.org/doi/10.14778/3311880.3311883
Rodríguez-Lorenzo EAdaricheva KCordero PEnciso MMora A(2017) Formation of the D -basis from implicational systems using Simplification logic International Journal of General Systems10.1080/03081079.2017.134963246:5(547-568)Online publication date: 28-Jul-2017
https://doi.org/10.1080/03081079.2017.1349632
Show More Cited By

Index Terms

Decompositions and functional dependencies in relations
1. Information systems
  1. Data management systems
    1. Database design and models
      1. Relational database model
    2. Query languages
      1. Relational database query languages

Recommendations

Normalization and hierarchical dependencies in the relational data model

The purpose of this paper is to present a new approach to the conceptual design of logical schemata for relational databases. One-to-one, one-to-many, and many-to-many relationships between the attributes of database relations are modeled by means of ...
Multivalued dependencies and a new normal form for relational databases

A new type of dependency, which includes the well-known functional dependencies as a special case, is defined for relational databases. By using this concept, a new (“fourth”) normal form for relation schemata is defined. This fourth normal form is ...
On the menbership problem for functional and multivalued dependencies in relational databases

The problem of whether a given dependency in a database relation can be derived from a given set of dependencies is investigated. We show that the problem can be decided in polynomial time when the given set consists of either multivalued dependencies ...

Comments

Information & Contributors

Information

Published In

cover image ACM Transactions on Database Systems

ACM Transactions on Database Systems Volume 5, Issue 4

Dec. 1980

128 pages

ISSN:0362-5915

EISSN:1557-4644

DOI:10.1145/320610

Editor:
David K. Hsiao
Ohio State Univ., Columbus

Issue’s Table of Contents

Copyright © 1980 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 December 1980

Published in TODS Volume 5, Issue 4

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Author Tags

Qualifiers

Article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

49
Total Citations
View Citations
1,356
Total Downloads

Downloads (Last 12 months)231
Downloads (Last 6 weeks)10

Reflects downloads up to 12 Feb 2025

Other Metrics

View Author Metrics

Citations

Cited By

Suciu D(2023)Applications of Information Inequalities to Database Theory Problems2023 38th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)10.1109/LICS56636.2023.10175769(1-30)Online publication date: 26-Jun-2023
https://doi.org/10.1109/LICS56636.2023.10175769
Kwashie SLiu LLiu JStumptner MLi JYang L(2019)CertusProceedings of the VLDB Endowment10.14778/3311880.331188312:6(653-666)Online publication date: 1-Feb-2019
https://dl.acm.org/doi/10.14778/3311880.3311883
Rodríguez-Lorenzo EAdaricheva KCordero PEnciso MMora A(2017) Formation of the D -basis from implicational systems using Simplification logic International Journal of General Systems10.1080/03081079.2017.134963246:5(547-568)Online publication date: 28-Jul-2017
https://doi.org/10.1080/03081079.2017.1349632
Turan UToroslu İKantarcıoğlu M(2017)Secure logical schema and decomposition algorithm for proactive context dependent attribute based inference controlData & Knowledge Engineering10.1016/j.datak.2017.02.002111(1-21)Online publication date: Sep-2017
https://doi.org/10.1016/j.datak.2017.02.002
Viaud JBertet KMissaoui RDemko C(2017)Distributed and Parallel Computation of the Canonical Direct BasisFormal Concept Analysis10.1007/978-3-319-59271-8_15(228-241)Online publication date: 19-May-2017
https://doi.org/10.1007/978-3-319-59271-8_15
Winter M(2016)Dependencies in relational models of databasesJournal of Logical and Algebraic Methods in Programming10.1016/j.jlamp.2015.12.00685:5(1095-1107)Online publication date: Aug-2016
https://doi.org/10.1016/j.jlamp.2015.12.006
Lee T(2013)An Algebraic Theory of Relational DatabasesBell System Technical Journal10.1002/j.1538-7305.1983.tb03470.x62:10(3159-3204)Online publication date: 29-Jul-2013
https://doi.org/10.1002/j.1538-7305.1983.tb03470.x
Link S(2011)On Inferences of Full First-Order Hierarchical DecompositionsFundamenta Informaticae10.5555/2351776.2351783106:2-4(233-258)Online publication date: 1-Apr-2011
https://dl.acm.org/doi/10.5555/2351776.2351783
Amalfi MArtale ACalì AProvetti A(2011)Generating preview Instances for the face validation of entity-relationship schemataProceedings of the 16th international conference on Database systems for advanced applications: Part II10.5555/1997251.1997272(225-234)Online publication date: 22-Apr-2011
https://dl.acm.org/doi/10.5555/1997251.1997272
Amalfi MArtale ACalì AProvetti A(2011)Generating Preview Instances for the Face Validation of Entity-Relationship Schemata: The Acyclic CaseDatabase Systems for Advanced Applications10.1007/978-3-642-20152-3_17(225-234)Online publication date: 2011
https://doi.org/10.1007/978-3-642-20152-3_17
Show More Cited By

View Options

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Article

Figures

Tables

Media

View Issue’s Table of Contents