Repetitions and permutations of columns in the semijoin algebra

Dirk Leinders; Jan Van Den Bussche

RAIRO - Theoretical Informatics and Applications (2008)

  • 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 ACM13 (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 Van Den Bussche, Jan. "Repetitions and permutations of columns in the semijoin algebra." RAIRO - Theoretical Informatics and Applications 43.2 (2008): 179-187. <http://eudml.org/doc/92910>.

@article{Leinders2008,
abstract = { Codd defined the relational algebra [E.F. Codd, Communications of the ACM13 (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, Van Den Bussche, Jan},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Database; relational algebra; semijoin algebra; projection.; database; projection},
language = {eng},
month = {6},
number = {2},
pages = {179-187},
publisher = {EDP Sciences},
title = {Repetitions and permutations of columns in the semijoin algebra},
url = {http://eudml.org/doc/92910},
volume = {43},
year = {2008},
}

TY - JOUR
AU - Leinders, Dirk
AU - Van Den Bussche, Jan
TI - Repetitions and permutations of columns in the semijoin algebra
JO - RAIRO - Theoretical Informatics and Applications
DA - 2008/6//
PB - EDP Sciences
VL - 43
IS - 2
SP - 179
EP - 187
AB - Codd defined the relational algebra [E.F. Codd, Communications of the ACM13 (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.; database; projection
UR - http://eudml.org/doc/92910
ER -

References

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  1. S. Abiteboul, R. Hull and V. Vianu, Foundations of Databases. Addison-Wesley (1995).  Zbl0848.68031
  2. H. Andréka, I. Németi and J. van Benthem, Modal languages and bounded fragments of predicate logic. J. Philosophical Logic27 (1998) 217–274.  Zbl0919.03013
  3. E.F. Codd, A relational model of data for large shared data banks. Communications of the ACM13 (1970) 377–387.  Zbl0207.18003
  4. E.F. Codd, Relational completeness of data base sublanguages, in Data Base Systems, R. Rustin, Ed. Prentice-Hall (1972) pp. 65–98.  
  5. E. Grädel, On the restraining power of guards. J. Symbolic Logic64 (1999) 1719–1742.  Zbl0958.03027
  6. E. Grädel, Guarded fixed point logics and the monadic theory of countable trees. Theor. Comput. Sci.288 (2002) 129–152.  Zbl1061.03022
  7. E. Grädel, C. Hirsch and M. Otto, Back and forth between guarded and modal logics. ACM Transactions on Computational Logic3 (2002) 418–463.  
  8. E. Grädel and I. Walukiewicz, Guarded fixed point logic, in Proceedings of the 14th IEEE Symposium on Logic in Computer Science LICS '99 (1999) pp. 45–54.  
  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.  Zbl1115.68066
  10. D. Leinders, M. Marx, J. Tyszkiewicz and J. Van den Bussche, The semijoin algebra and the guarded fragment. J. Logic, Language and Information14 (2005) 331–343.  Zbl1080.03012
  11. D. Leinders, J. Tyszkiewicz and J. Van den Bussche, On the expressive power of semijoin queries. Inform. Process. Lett.91 (2004) 93–98.  Zbl1178.68202

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