Advances in Data Base Theory: Volume 2 by Joachim Biskup, Hans Hermann Brüggemann (auth.), Hervé

By Joachim Biskup, Hans Hermann Brüggemann (auth.), Hervé Gallaire, Jack Minker, Jean Marie Nicolas (eds.)

This is the 3rd e-book dedicated to theoretical concerns in information­ bases that we have got edited. each one e-book has been the outgrowth of papers held at a workshop in Toulouse, France. the 1st workshop, held in 1977 targeted totally on the real subject of good judgment and databases. The booklet, good judgment and Databases used to be the results of this attempt. the various makes use of of good judgment for databases comparable to its use as a theoretical foundation for databases, for deduction and for integ­ rity constraints formula and checking used to be defined within the chapters of the e-book. The curiosity generated by way of the 1st workshop ended in the deci­ sion to behavior different workshops excited by theoretical concerns in databases. as well as common sense and databases the kinds of papers have been accelerated to incorporate different vital theoretical matters corresponding to dependency thought which, even though it occasionally makes use of good judgment as a foundation, doesn't healthy with our meant that means of common sense and databases explored on the first workshop. end result of the broader insurance, and since we expected additional workshops, the second one e-book used to be entitled, Advances in Database concept - quantity 1. The e-book "Logic and Databases" can be thought of quantity zero of this series.

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Ullman, J. D. [1~82] Principles of Database Systems, Second Edition, Computer Science Press, Potomac, Maryland (1982). 23. Ullman, J. D. [1983] "Universal relation interfaces for database systems", unpublished manuscript, Dept. of Computer Science, Stanford University, Stanford, California (1983). 24. Yannakakis, M. [1981] "Algorithms for acylic database schemes", Proceedings 7th Conference on Very Large Data Bases, Cannes, France (September 1981) 82-94. ELIMINATING CYCLES IN DATABASE SCHEMAS Yoshito Hanatani Institut National de Recherche en Informatique et en Automatique, Rocquencourt, France ABSTRACT Call J-schema (respectively M-schema) a schema that can be described by a single jOin-dependency (respectively by a set of multi-valued dependencies).

Furthermore define for j E Nl [j] := {i I iE NO' and there exists k > 0 with reducek(i) = j} (where reduceO(i) := i, reducek+l(i) :=reducek(reduce(i»). 19 TOWARDS DESIGNING ACYCLIC DATABASE SCHEMES Then we have: E [j] and NO LJ (1) j (2) For every A E W(NO) \ W(NI ) there exists p E NI such that rel(A) := {i I iE NO' and A E Ri } C [p] • (3) If mE [p] then Rm n w(Nl ) C wNI (p). Proof: = [j ] • jENI (1) Follows from the definitions. (2) First we note that Orel(A) n NIH ~ 1, (17) for otherwise, if i,j E rel(A) n NI , i # j, then A E R.

And Shmueli, o. [1983] "Syntactic Characterizations of Tree Database Schemas", Journal of the ACM, to appear. 11. Graham, M. H. [1979] "On the Universal Relation", Technical Report, University of Toronto. 12. Gyssens, M. and Paredaens, J. [1984] "A Decomposition Methodology for Cyclic Databases", In: Advances in Database Theory, Volume 2 (H. Gallaire, J. -M. ), Plenum Press, (1984) 85-107. 13. Hanatani, Y. [1984] "Eliminating Cycles in Database Schemas", In: Advances in Database Theory, Vol. 2 (H.

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