No abstract

A class of dependencies, tuple and equality generating dependencies, is defined, and the chase process is generalized to deal with these dependenetes. For total dependencies the chase is an exponential ttme decision procedure for the implication problem, and in some restricted cases it can be modified to run m polynomial Ume. For nontotal dependencies the chase is only a proof procedure. However, several cases for which it is a decision procedure are shown. It is also shown that equality is redundant for deciding implication of tuple-generating dependencies, and is "almost redundant" for dec~ding implication of equality-generating dependencies.

Problems related to functional dependencies and the algorithmic design of relational schemas are examined. Specifically, the following results are presented: (1) a tree model of derivations of functional dependencies from other functional dependencies; (2) a linear-time algorithm to test if a functional dependency is in the closure of a set c,f functional dependencies; (3) a quadratic-time implementation of Bernstein's third normal form schema synthesis algorithm.Furthermore, it is shown that most interesting algorithmic questions about Boyce-Codd normal form and keys are &?-complete and are therefore probably not amenable to fast algorithmic solutions.

No abstract

No abstract