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In relational algebra, a recursive relation R is defined by an equation of the form R = f(R), where f(R) is a positive relational algebra expression. Such an equation can be solved by applying a general closure operator. Although some optimization is possible, the performance obtained using this approach is very dependent on the form of the equation which defines R. Principally for this reason, we have developed specialized closure operators for relations which are solutions to problems of practical importance such as transitive closure, accessibility, shortest path, bill-of-materials, and deductions by containment comparisons. / This approach has led to the following general results: (1) design, classification, and analysis of many iterative methods for evaluating recursive relations, as well as analysis of experimental results; (2) formalization of the concept of iterative evaluation of a relation; (3) demonstration that domain algebra can be used to solve problems of concatenation and aggregation of the information associated with a recursive structure; (4) proof that relational division and general containment joins are left-monotone. / More specific results consist of a collection of original algorithms which run well on secondary storage, as shown by simulations. Among them, we wish to emphasize the differencing logarithmic transitive closure (TC) algorithms, which are superior to the previously known relational TC algorithms, and the shortest path algorithms, which are in fact generic algorithms for path algebra problems.

Thesis (M.A.)--York University, 2006. Graduate Programme in Philosophy. / Typescript. Includes bibliographical references (leaves 125-133). Also available on the Internet. MODE OF ACCESS via web browser by entering the following URL: http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&res_dat=xri:pqdiss&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&rft_dat=xri:pqdiss:MR29605

Thesis (doctoral)--Rijksuniversiteit te Utrecht, 1971. / "Stellingen" ([2] p.) inserted. Summary in Dutch. Includes supplementary part II to the author's thesis. Includes bibliographical references (p. 134-138).

Thesis (doctoral)--Rijksuniversiteit te Utrecht, 1971. / "Stellingen" ([2] p.) inserted. Summary in Dutch. Includes supplementary part II to the author's thesis. Includes bibliographical references (p. 134-138).

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Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1980. / Vita. / Bibliography: leaves 161-163. / by Edward R. Griffor. / Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1980.