Dezsö Miklós

Asymptotic properties of keys and functional dependencies in random databases

Abstract Practical database applications give the impression that sets of constraints are rather small and that large sets are unusual and are caused by bad design decisions. Theoretical investigations, however, show that minimal constraint sets are potentially very large. Their size can be estimated to be exponential in terms of the number of attributes. The gap between observation in practice and theory results in the rejection of theoretical results. However, practice is related to average cases and is not related to worst cases. The theory used until now considered the worst-case complexity. This paper aims to develop a theory for the average-case complexity . Several probabilistic models and asymptotics of corresponding probabilities are investigated for random databases formed by independent random tuples with a common discrete distribution. Poisson approximations are studied for the distributions of some characteristics for such databases where the number of tuples is sufficiently large. We intend to prove that the exponential complexity of key sets and sets of functional dependencies is rather unusual and almost all minimal keys in a relation have a length which depends mainly on the size of the relation.

The Average Length of Keys and Functional Dependencies in (Random) Databases

Practical database applications engender the impression that sets of constraints are rather small and that large sets are unusual and caused by bad design decisions. Theoretical investigations show, however, that minimal constraint sets are potentially very large. Their size can be estimated to be exponential in terms of the number of attributes. The gap between belief and theory causes non-acceptance of theoretical results. However, beliefs are related to average cases.

Partial dependencies in relational databases and their realization

Abstract Weakening the functional dependencies introduced by Amstrong we get the notion of the partial dependencies defined on the relational databases. We show that the partial dependencies can be characterized by the closure operations of the poset formed by the partial functions on the attributes of the databases. On the other hand, we give necessary and sufficient conditions so that for such a closure operation one can find on the given set of attributes a database whose partial dependencies generate the given closure operation. We also investigate some questions about how to realize certain structures related to databases by a database of minimal number of rows, columns or elements.

Functional Dependencies in Presence of Errors

A relational database D is given with ? as the set of attributes. The rows (tuples, data of one individual) are transmitted through a noisy channel. It is supposed that at most one data in a row can be changed by the transmission. We say that A ? b (A ? ?, b ? ?) is an error-correcting functional dependency if the data in A uniquely determine the data in b in spite of the error. We investigate the problem how much larger a minimal error-correcting functional dependency can be than the original one.

Error-Correcting Keys in Relational Databases

Suppose that the entries of a relational database are collected in an unreliable way, that is the actual database may differ from the true database in at most one data of each individual. An error-correcting key is such a set of attributes, that the knowledge of the actual data of an individual in this set of attributes uniquely determines the individual. It is showed that if the minimal keys are of size at most k, then the smallest sizes of the minimal error-correcting keys can be ck3 and this is the best possible, all minimal error-correcting keys have size at most 3k3.

On the security of individual data

We will consider the following problem in this paper: Assume that there are

The addition game: an abstraction of a communication problem

n

On the number of independent functional dependencies

numerical data