Conjunctive Query Equivalence of Keyed Relational Schemas.

The notion of when two schemas are equivalent is fimdamental to database design, schema integration, and data model translation. An important notion of schema equivalence, query equivalence was introduced in [3], and used to evaluate the correctness of schema transformations. The logically equivalent notion of calculous equivalence, as well as three progressively weaker notions of schema equivalence were introduced in 1984 by Hull [9, lo], who showed that two schemas with no dependencies are equivalent (under all four notions of equivalence) if and only if they are identical (up to renaming and re-ordering of attributes and relations). Hull also conjectured that the same result holds for schemas with primary keys. In this work, we resolve the conjecture in the affirmative for the case of query equivalence based on mappings using conjunctive relational queries with equality selections.

[1]  E. F. Codd,et al.  Further Normalization of the Data Base Relational Model , 1971, Research Report / RJ / IBM / San Jose, California.

[2]  C. Robert Carlson,et al.  The Information Preserving Properties of Relational Database Transformations , 1978, VLDB.

[3]  Catriel Beeri,et al.  A Sophisticate's Introduction to Database Normalization Theory , 1978, VLDB.

[4]  David Maier,et al.  Adequacy of Decompositions of Relational Databases , 1980, J. Comput. Syst. Sci..

[5]  Tok Wang Ling,et al.  An improved third normal form for relational databases , 1981, TODS.

[6]  Catriel Beeri,et al.  Equivalence of Relational Database Schemes , 1981, SIAM J. Comput..

[7]  Carlo Batini,et al.  Inclusion and Equivalence between Relational Database Schemata , 1982, Theor. Comput. Sci..

[8]  Jorma Rissanen.  On equivalences of database schemes , 1982, PODS '82.

[9]  Carlo Zaniolo.  A new normal form for the design of relational database schemata , 1982, TODS.

[10]  E. F. Codd,et al.  A relational model of data for large shared data banks , 1970, CACM.

[11]  C. Batini,et al.  A comparative analysis of methodologies for database schema integration , 1986, CSUR.

[12]  Richard Hull.  Relative Information Capacity of Simple Relational Database Schemata , 1986, SIAM J. Comput..

[13]  Arnon Rosenthal,et al.  Theoretically Sound Transformations for Practical Database Design , 1987, ER.

[14]  A. Sheth.  Federated database systems for managing distributed, heterogeneous, and autonomous databases , 1990, CSUR.

[15]  Renée J. Miller,et al.  The Use of Information Capacity in Schema Integration and Translation , 1993, VLDB.