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

This is the 3rd ebook dedicated to theoretical concerns in info bases that we have got edited. every one booklet has been the outgrowth of papers held at a workshop in Toulouse, France. the 1st workshop, held in 1977 concentrated totally on the real subject of common sense 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 similar 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 all for theoretical concerns in databases. as well as good judgment and databases the kinds of papers have been increased to incorporate different vital theoretical concerns corresponding to dependency concept 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. a result of broader assurance, and since we expected additional workshops, the second one publication was once entitled, Advances in Database conception - quantity 1. The publication "Logic and Databases" may be thought of quantity zero of this series.

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Maier, D. and Ullman, J. D. [1982] "Connections in acyclic hypergraphs", Proceedings First SIGACT-SIGMOD Symposium on Principles of Database Systems, Los Angeles, California (March 1982) 34-39. 20. Osborn, S. L. [1979] "Towards a universal relation interface", Proceedings 5th Conference on Very Large Data Bases, Rio de Janeiro, Brazil (October 1979) 52-60. MINIMAL COVERINGS OF ACYCLIC SCHEMATA 51 21. Paredaens, J. and Van Gucht, D. [1983] "An application of the theory of graphs and hypergraphs to the decomposition of relational database schemes", Proceedings 8th Colloquium on Trees in Algebra and Programming, L'Aquila, Italy (March 1983), to appear in Lecture Notesin Computer Science, Springer Verlag.

Paredaens, the Theory Relational Colloquium Italy. 18. Sacca, D. [1982] "Closure of Database Hypergraphs", IBM Research Report, RJ 3723 (42939), San Jose, California. 19. Ullman, J. D. [1980] Principles of Database Systems, Computer Science Press, Potomac, Maryland. , and van Gucht, D. [1983] "An Application of of Graphs and Hypergraphs to the Decomposition of Database Schemas", Proceedings CAAP 83, 8th on Trees in Algebra and programming, L'Aquila, MINIMAL COVERINGS OF ACYCLIC DATABASE SCHEMATA G.

E q > is a pure cycle (Fagin [1982]) if q= 3 and el n e2 n e3 = ~ or i f q > 3 and for all pairs i,j (l~ i~ q and 1 ~ j ~ q) such that 1 < li-j I < q-l we have that ei n e j = ~. (The hypergraph in Figure 1 has the pure cycle <{A,B,C,N},{C,N,D,E},{A,E,F}». This definition of pure cycle is the strongest, and probably, the most natural and noncontroversial definition of cycle in a hypergraph; in fact it is easy to prove that this type of cyclicity is included in all existing definitions of cycle in the literature.