Proof-tree transformation theorems and their applications

  • Authors:
  • R. Ramakrishnan;Y. Sagiv;J. D. Ullman;M. Y Vardi

  • Affiliations:
  • University of Wisconsin;Hebrew University;Stanford University;IBM Almaden Research Center

  • Venue:
  • PODS '89 Proceedings of the eighth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
  • Year:
  • 1989

Quantified Score

Hi-index 0.00

Visualization

Abstract

For certain sets of logical rules, one can demonstrate that for every proof tree there is another tree proving the same fact and having a special form. One technique for detecting such opportunities is to reduce the question to one of conjunctive-query containment. A more powerful technique is to test whether one conjunctive query is contained in the infinite union of conjunctive queries formed by expanding a set of recursive rules. We discuss two applications of these techniques. First, we give tests for commutativity of linear rules. When linear rules commute, we can reduce the complexity of “counting” methods for query evaluation from exponential to polynomial; commutativity also implies separability in the sense of Naughton. A second application is the discovery of linear rules that are equivalent to given nonlinear rules.