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Polynomial tests of normal forms and some related results

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Abstract

The following problem is called the everywhere-cover problem: “Given a set of dependencies over a database schemen, is the set of dependencies explicitly given for each relation scheme equivalent to the dependencies implied for that relation scheme?” It is shown that when the everywhere-cover problem has a ‘yes’ answer, examining only the dependencies explicitly given will suffice to test 3NF, BCNF and 4NF of a database scheme. But this does not hold for 2NF. Consequently, in such cases, tests of BCNF and 4NF all take polynomial time. Then a proof is given that test of 3NF of a database scheme is Co-NP-complete, and from this result it is shown that everywhere-cover is also Co-NP-complete when only functional dependencies are allowed. These results lead to doubt the truth of the well believed conjecture that no polynomial time algorithm for designing a lossless BCNF database scheme is likely to exist.

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References

  1. E. F. Codd, A relational model for large shared data banks.CACM, 1970, 13(6), 377–387.

    MATH  Google Scholar 

  2. E. F. Codd, Further normalization of the data base relational model. Data Base System (R. Rustin, ed.), 1972, 33–64.

  3. R. Fagin, Multivalued dependencies and a new normal form for relational databases.ACM TODS, 1977, 2(3), 262–278.

    Article  Google Scholar 

  4. R. Fagin, The decomposition versus synthetic approach to relational database design. VLDB, 1977, 441–446.

  5. D. Maier, The theory of relational databases. CSP, Inc., 1983.

  6. J.D. Ullman, Principles of database systems. CSP, Inc., 1982.

  7. J. Biskup, U. Dayal and P. Bemstein, Synthesizing independent database schemes. ACM SIGMOD, 1979, 143–151.

  8. P.A. Bernstein, Synthesizing third normal form relations from functional dependencies.ACM TODS, 1976, 1(4), 272–298.

    Article  Google Scholar 

  9. W.W. Armstrong, Dependency structures of data base relationships. IFIP, 1974, 580–583.

  10. C. Beeri, R. Fagin and J. H. Howard, A complete axiomatization for functional and multivalued dependencies. ACM SIGMOD, 1977, 47–61.

  11. C. L. Lucchesi and S. L. Osborne, Candidate keys for relations.JCSS Vol., 1978, 270–279.

  12. C. Beeri and P.A. Bemstein, Computational problems related to the design of normal form relation schemes.ACM TODS, 1979, 4(1), 30–59.

    Article  Google Scholar 

  13. Jou, Jiann H. and Fischer, Patrick C., The complexity of recognizing 3NF relation schemes.Information Processing Letters, 1982, 14(4), 187–190.

    Article  MATH  MathSciNet  Google Scholar 

  14. R.M. Karp, Reducibility Among Combinatorial Problems. in: Complexity of Computer Computations (Plenum Press, New York 1972), 85–104.

    Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science, Chongqing University, 630044, Chongqing

    Ke Wang

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  1. Ke Wang
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Supported by the National Natural Science Foundation of China.

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Wang, K. Polynomial tests of normal forms and some related results. J. of Comput. Sci. & Technol. 7, 75–82 (1992). https://doi.org/10.1007/BF02946169

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  • DOI: https://doi.org/10.1007/BF02946169

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