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

Abstract

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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.

How to cite

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Leinders, 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 -

References

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  9. [9] D. Leinders and J. Van den Bussche, On the complexity of division and set joins in the relational algebra. J. Comput. Syst. Sci. 73 (2007) 538–549. Special issue with selected papers on database theory. Zbl1115.68066MR2320184
  10. [10] D. Leinders, M. Marx, J. Tyszkiewicz and J. Van den Bussche, The semijoin algebra and the guarded fragment. J. Logic, Language and Information 14 (2005) 331–343. Zbl1080.03012MR2167027
  11. [11] D. Leinders, J. Tyszkiewicz and J. Van den Bussche, On the expressive power of semijoin queries. Inform. Process. Lett. 91 (2004) 93–98. Zbl1178.68202MR2064649

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