Abstract

I authorize the University of Waterloo to lend this thesis to other institutions or individuals for the purpose of scholarly research. I further authorize the University of Waterloo to reproduce this thesis by photocopying or by other means, in total or in part, at the request of other institutions or individuals for the purpose of scholarly research. iii The University of Waterloo requires the signatures of all persons using or photocopying this thesis. Please sign below, and give address and date. Functional dependency analysis can be applied to various problems in query optimization: selectivity estimation, estimation of (intermediate) result sizes, order optimization (in particular sort avoidance), cost estimation, and various problems in the area of semantic query optimization. Dependency analysis in an ansi sql relational model, however, is made complex due to the existence of null values, three-valued logic, outer joins, and duplicate rows. In this thesis we define the notions of strict and lax functional dependencies, strict and lax equivalence constraints, and null constraints, which capture both a

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