# Repetitions and permutations of columns in the semijoin algebra

Dirk Leinders; Jan Van Den Bussche

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (2009)

- Volume: 43, Issue: 2, page 179-187
- ISSN: 0988-3754

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topLeinders, Dirk, and Jan Van Den Bussche. "Repetitions and permutations of columns in the semijoin algebra." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 43.2 (2009): 179-187. <http://eudml.org/doc/245912>.

@article{Leinders2009,

abstract = {Codd defined the relational algebra [E.F. Codd, Communications of the ACM 13 (1970) 377–387; E.F. Codd, Relational completeness of data base sublanguages, in Data Base Systems, R. Rustin, Ed., Prentice-Hall (1972) 65–98] as the algebra with operations projection, join, restriction, union and difference. His projection operator can drop, permute and repeat columns of a relation. This permuting and repeating of columns does not really add expressive power to the relational algebra. Indeed, using the join operation, one can rewrite any relational algebra expression into an equivalent expression where no projection operator permutes or repeats columns. The fragment of the relational algebra known as the semijoin algebra, however, lacks a full join operation. Nevertheless, we show that any semijoin algebra expression can still be simulated in a natural way by a set of expressions where no projection operator permutes or repeats columns.},

author = {Leinders, Dirk, Jan Van Den Bussche},

journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},

keywords = {database; relational algebra; semijoin algebra; projection},

language = {eng},

number = {2},

pages = {179-187},

publisher = {EDP-Sciences},

title = {Repetitions and permutations of columns in the semijoin algebra},

url = {http://eudml.org/doc/245912},

volume = {43},

year = {2009},

}

TY - JOUR

AU - Leinders, Dirk

AU - Jan Van Den Bussche

TI - Repetitions and permutations of columns in the semijoin algebra

JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

PY - 2009

PB - EDP-Sciences

VL - 43

IS - 2

SP - 179

EP - 187

AB - Codd defined the relational algebra [E.F. Codd, Communications of the ACM 13 (1970) 377–387; E.F. Codd, Relational completeness of data base sublanguages, in Data Base Systems, R. Rustin, Ed., Prentice-Hall (1972) 65–98] as the algebra with operations projection, join, restriction, union and difference. His projection operator can drop, permute and repeat columns of a relation. This permuting and repeating of columns does not really add expressive power to the relational algebra. Indeed, using the join operation, one can rewrite any relational algebra expression into an equivalent expression where no projection operator permutes or repeats columns. The fragment of the relational algebra known as the semijoin algebra, however, lacks a full join operation. Nevertheless, we show that any semijoin algebra expression can still be simulated in a natural way by a set of expressions where no projection operator permutes or repeats columns.

LA - eng

KW - database; relational algebra; semijoin algebra; projection

UR - http://eudml.org/doc/245912

ER -

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