By Antje Düsterhöft, Meike Klettke, Klaus-Dieter Schewe

This Festschrift, released in honor of Bernhard Thalheim at the get together of his sixtieth birthday offers 20 articles by way of colleagues from worldwide with whom Bernhard Thalheim had cooperation in a variety of respects; additionally integrated is a systematic biography contributed by means of the quantity editors. The 20 contributions replicate the breadth and the intensity of the paintings of Bernhard Thalheim in conceptual modeling and database concept in the course of his clinical occupation spanning greater than 35 years of energetic learn. particularly, ten articles are targeting subject matters like database dependency conception, object-oriented databases, triggers, summary kingdom machines, database and knowledge structures layout, internet semantics, and enterprise processes.

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Asymptotic properties of keys and functional dependencies in random databases. Theor. : Functional dependencies in random databases. Studia Scien. Math. : Probability: Theory and Examples. : Maximum-entropy Models in Science and Engineering. : Entropy Optimization Principles with Applications. : Database Systems: An Application-Oriented Approach. : Theory of U -statistics. : On statistical estimation of entropy of random vector. Problems Infor. Transmiss. : U -Statistics: Theory and Practice.

Dependent attributes extremal attributes independent attributes I1 (1-prime) D E (nonprime) (superprime) (nonprime) K1 K2 I2 (1-prime) Fig. 1. Dependency structure of schemes having exactly two minimal keys Schemes Having Few Minimal Keys 25 Theorem 1. Let RS = U, Σ be a scheme. Then RS has exactly two minimal keys K1 = K2 iﬀ (1) Σ[E] = U , and (2) ∼mk has exactly two equivalence classes ˙ 1 and K2 = E ∪I ˙ 2, I1 and I2 that are diﬀerent from E and N , and (3) K1 = E ∪I and thus then I1 = K1 \ K2 and I2 = K2 \ K1 .

Let A ⊂ Ω, b ∈ Ω, b ∈ A. The random vector of the coordinates ξi (i ∈ A) will be denoted by α. The probability of the event that α is equal to the kth sequence is denoted by pk (A). Moreover, the probability of the event that α is equal to the kth sequence and ξb has the th entry is pk, (A, b). Our crucial notion is deﬁned in the following way: H2 (A → b) = H2 (α → ξb ). (3) The Heuristic Version of the Theorem. The functional dependency A → b ”seems to hold” (there are no two rows equal in the entries belonging to A and diﬀerent in the column of b) with large probability in a random database of size m if and only if 2 log2 m is much smaller than H2 (A → b).