Repetitions and permutations of columns in the semijoin algebra
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 43 (2009) no. 2, pp. 179-187.

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.

DOI : https://doi.org/10.1051/ita:2008023
Classification : 68P15
Mots clés : database, relational algebra, semijoin algebra, projection
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     title = {Repetitions and permutations of columns in the semijoin algebra},
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Leinders, Dirk; Jan Van Den Bussche. Repetitions and permutations of columns in the semijoin algebra. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 43 (2009) no. 2, pp. 179-187. doi : 10.1051/ita:2008023. http://www.numdam.org/articles/10.1051/ita:2008023/

[1] S. Abiteboul, R. Hull and V. Vianu, Foundations of Databases. Addison-Wesley (1995). | Zbl 0848.68031

[2] H. Andréka, I. Németi and J. Van Benthem, Modal languages and bounded fragments of predicate logic. J. Philosophical Logic 27 (1998) 217-274. | MR 1624137 | Zbl 0919.03013

[3] E.F. Codd, A relational model of data for large shared data banks. Communications of the ACM 13 (1970) 377-387. | Zbl 0207.18003

[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 Logic 64 (1999) 1719-1742. | MR 1780081 | Zbl 0958.03027

[6] E. Grädel, Guarded fixed point logics and the monadic theory of countable trees. Theor. Comput. Sci. 288 (2002) 129-152. | MR 1934892 | Zbl 1061.03022

[7] E. Grädel, C. Hirsch and M. Otto, Back and forth between guarded and modal logics. ACM Transactions on Computational Logic 3 (2002) 418-463. | MR 1911554

[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. | MR 1942519

[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. | MR 2320184 | Zbl 1115.68066

[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. | MR 2167027 | Zbl 1080.03012

[11] D. Leinders, J. Tyszkiewicz and J. Van Den Bussche, On the expressive power of semijoin queries. Inform. Process. Lett. 91 (2004) 93-98. | MR 2064649 | Zbl 1178.68202

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