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Determining View dependencies using tableaux

Published:01 September 1982Publication History
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Abstract

A relational database models some part of the real world by a set of relations and a set of constraints. The constraints model properties of the stored information and must be maintained true at all times. For views defined over physically stored (base) relations, this is done by determining whether the view constraints are logical consequences of base relation constraints. A technique for determining such valid view constraints is presented in this paper. A generalization of the tableau chase is used. The idea of the method is to generate a tableau for the expression whose summary violates the test constraints in a “canonical” way. The chase then tries to remove this violation.

It is also shown how this method has applications to schema design. Relations not in normal form or having other deficiencies can be replaced by normal form projections without losing the ability to represent all constraint information.

References

  1. 1 AHO, A.V., BEERI, C., AND ULLMAN, J.D. The theory of joins in relational databases. A CM Trans. Database Syst. 4, 3 (Sept. 1979), 297-314. Google ScholarGoogle ScholarDigital LibraryDigital Library
  2. 2 AHO, A.V., SAGIV, Y., AND ULLMAN, J.D. Equivalences among relational expressions. SIAM J. Comput. 8, 2 (May 1979), 218-246.Google ScholarGoogle ScholarCross RefCross Ref
  3. 3 BEERI, C., AND VARDI, M.Y. The implication problem for data dependencies. Preliminary rep., The Hebrew Univ. of Jerusalem, 1980.Google ScholarGoogle Scholar
  4. 4 BEERI, C., BERNSTEIN, P., AND GOODMAN, N. A sophisticate's introduction to database normalization theory. In Proc. Fourth int. Conf. on Very Large Data Bases. West Berlin, Sept. 13- 15, 1978, pp. 113-124.Google ScholarGoogle Scholar
  5. 5 BERNSTEIN, P.A. Synthesizing third normal form relations from functional dependencies. ACM Trans. Database Syst. 1, 4 (1976), 271-298. Google ScholarGoogle ScholarDigital LibraryDigital Library
  6. 6 BERNSTEIN, P.A., AND GOODMAN, N. What does Boyce-Codd normal form do? In Proc. Sixth Int. Conf. on Very Large Data Bases, Montreal, Oct. 1-3, 1980, pp. 245-259.Google ScholarGoogle ScholarDigital LibraryDigital Library
  7. 7 CHANDRA, A.K., AND MERLIN, P.M. Optimal implementation of conjunctive queries in relational databases. In Proc. Ninth Annual Syrup. on Theory of Computing, Boulder, Colo., May 2-4, 1976, ACM, New York, pp. 77-90. Google ScholarGoogle ScholarDigital LibraryDigital Library
  8. 8 CODD, E.F. A relational model of data for large shared data banks. Commun. ACM 13, 6 (June 1970), 377-387. Google ScholarGoogle ScholarDigital LibraryDigital Library
  9. 9 CODD, E.F. "Relational Completeness of Data Base Sublanguages." In Data Base Systems, edited by R. Rustin, Prentice Hall, Englewood Cliffs, N.J., 1972.Google ScholarGoogle Scholar
  10. 10 FACIN, R. Multivalued dependencies and a new normal form for relational databases. ACM Trans. Database Syst. 2, 3 (Sept. 1977), 262-278. Google ScholarGoogle ScholarDigital LibraryDigital Library
  11. 11 FA6IN, R. Normal forms and relational database operators. In Proc. ACM-SIGMOD Int. Conf. on Management of Data, Boston, May 30-June 1, 1979, pp. 153-160. Google ScholarGoogle ScholarDigital LibraryDigital Library
  12. 12 GRAHAM, M.H. A new proof that the chase is a Church-Rosser process. In Proc. XP1 Workshop on Relational Database Theory, Stonybrook, N.Y.Google ScholarGoogle Scholar
  13. 13 GRANT, J. AND JACOBS, B. On generalized dependency statements. J. ACM, in press. Google ScholarGoogle ScholarDigital LibraryDigital Library
  14. 14 GRIFFITHS, P., AND WADE, B.W. An authorization mechanism for a relational database system. ACM Trans. Database Syst. I, 3 (Sept. 1976), 242-255. Google ScholarGoogle ScholarDigital LibraryDigital Library
  15. 15 JACOBS, B.E., ARONSON, A.R., AND KLUG, A. On interpretations of relational languages and solutions to the implied constraint problem. ACM Trans. Database Syst., in press. Google ScholarGoogle ScholarDigital LibraryDigital Library
  16. 16 KLUG, A. Calculating constraints on relational expressions. A CM Trans. Database Syst. 5, 3 (Sept. 1980), 260-290. Google ScholarGoogle ScholarDigital LibraryDigital Library
  17. 17 KLUG, A. Multiple view, multiple data model support in the cheops DBMS. To appear.Google ScholarGoogle Scholar
  18. 18 MAIER, D., MENDELZON, A.0., AND SAGIV, Y. Testing implications of data dependencies. ACM Trans. Database Syst. 4, 4 (Dec. 1979), 455-469. Google ScholarGoogle ScholarDigital LibraryDigital Library
  19. 19 NICOLAS, J.M. Mutual dependencies and some results on undecomposable relations. In Proc. Fourth Int. Conf. on Very Large Data Bases, West Berlin, Sept. 13-15, 1978, pp. 360-367.Google ScholarGoogle ScholarDigital LibraryDigital Library
  20. 20 RISSANEN, J. Theory of relations for databases--a tutorial survey. In Proc. Seventh Symp. on Math. Foundations of Computer Science, Lecture Notes in Computer Science 64, Springer- Verlag, New York, 1978, pp. 538-551.Google ScholarGoogle Scholar
  21. 21 SAGIV, Y. AND YANNAKAKIS, M. Equivalences among relational expressions with union and difference operators. J. ACM, 27, 4 (Oct. I980), 633-655. Google ScholarGoogle ScholarDigital LibraryDigital Library
  22. 22 SETHI, R. Testing for the Church-Rosser property. J. ACM 21, 4 (Oct. 1974), 671-679. Google ScholarGoogle ScholarDigital LibraryDigital Library
  23. 23 STONEBRAKER, M. Implementation of integrity constraints and views by query modifications. In Proc. ACM-SIGMOD Int. Conf. on Management of Data, San Jose, Calif., May 14-16, 1975, ACM, New York, pp. 65-78. Google ScholarGoogle ScholarDigital LibraryDigital Library
  24. 24 ULLMAN, J.{). Principles of Database Systems. Computer Science Press, Potomac, Md., i980. Google ScholarGoogle ScholarDigital LibraryDigital Library

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