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

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

ISBN-10: 1461593859

ISBN-13: 9781461593850

ISBN-10: 1461593875

ISBN-13: 9781461593874

This is the 3rd ebook dedicated to theoretical concerns in facts­ bases that we've got edited. every one ebook 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 publication, good judgment and Databases was once the results of this attempt. the varied 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 via the 1st workshop ended in the deci­ sion to behavior different workshops interested in theoretical matters in databases. as well as common sense and databases the categories of papers have been increased to incorporate different vital theoretical matters resembling dependency concept which, even though it occasionally makes use of common sense as a foundation, doesn't healthy with our meant that means of common sense and databases explored on the first workshop. as a result of the broader assurance, and since we expected additional workshops, the second one ebook used to be entitled, Advances in Database conception - quantity 1. The booklet "Logic and Databases" will be thought of quantity zero of this series.

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K, and eO = {N 1 1 e. U {nO,n i }, 1 U {nO""'~+l}}' Such a hypergraph is connected (nO belongs to every e E E) and is a-acyclic (eO contains every intersection of two edges in E). Besides no solution of the node-minimum covering problem can contain eO' It is ea~ to see that if H' = is a solution of this problem then E' = {e! } I e! E E'} is a solution of the corresponding MIN-SET-COVERINt problem. In the case of size-minimum coverings and node-minimum coverings, if we further enforce the acyclicity condition, the problem also becomes simpler.

K In order to prove fact (b) it is enough to observe that since the same arguments as before may be applied to all pairs of intersections of ei with adjacent edges, we must conclude that e must have the same intersections as ei with all other edges of H'. Furthermore ek must have the same ~ubset of nodes in N as ei, otherwise there should be two nodes in N connected by paths with different length. Hence e k would be redundant in H', and fact (b) is proved. k Fact (c). e k does not correspond to any edge other than ei.

In other words, the constraint jv is orthogonal (or independent) to the constraint M and therefore to j. On the other hand, the set of MVDs induced on U by j2 is equivalent to the set M' = {AC ++ BEF, BD ++ CFG}, and is strictly stronger than the set M. e. to j).

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Advances in Data Base Theory: Volume 2 by Joachim Biskup, Hans Hermann Brüggemann (auth.), Hervé Gallaire, Jack Minker, Jean Marie Nicolas (eds.)


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