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The equivalence problem for relational database schemes

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MFDBS 87 (MFDBS 1987)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 305))

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Abstract

Mappings between the sets of instances of database schemes are used to define different degrees of equivalence. The available class of mappings and the set of dependencies allowed for defining schemes deal here as parameters. A comparison of the equivalences shows that there is only one natural kind of equivalence. For various cases we prove its decidability or undecidability. Besides we get a characterization of mappings expressible in the relational algebra without the difference.

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References

  1. G. Ausiello, C. Batini, M. Moscarini: ‘Conceptual relations between databases transformed under join and projection's in: Proc. Symp. Math. Found. of Comp. Sc., 9, 1980, pp. 123–136

    Google Scholar 

  2. P. Atzeni, G. Aussiello, C. Batini, M. Moscarini: ‘Inclusion and equivalence between relational database schemes', in: Theoretical Computer Science, 19, 1982, pp. 267–285

    Google Scholar 

  3. P. Atzeni, D.S. Parker: ‘Assumptions in relational database theory', in: ACM Symp. on Princ. of Database Systems, 1, 1982, pp. 1–9

    Google Scholar 

  4. A.V. Aho, Y. Sagiv, J.D. Ullman: ‘Equivalences among relational expressions', in: SIAM Journ. of Computing, 8, 1979, pp. 218–246

    Google Scholar 

  5. A.V. Aho, J.D. Ullman: ‘Universality of data retrieval languages', in: ACM Symp. on Princ. of Programming Languages, 6, 1979, pp. 110–117

    Google Scholar 

  6. S.Abiteboul, V.Vianu: ‘Transactions in relational databases', in: Proc. ACM Int. Conf. on Very Large Data Bases, 1984

    Google Scholar 

  7. F. Bancilhon: ‘On the completeness of query languages for relational data bases', in: Proc. Symp. Math. Found. of Computer Science, 7, 1978, pp. 112–123

    Google Scholar 

  8. P.A. Bernstein, C. Beeri, N. Goodman: ‘A sophisticated introduction to database normalization theory', in: Proc. ACM Int. Conf. on Very Large Data Bases, 4, 1978, pp. 113–124

    Google Scholar 

  9. H. Biller: ‘On the equivalence of database schemes — a semantic approach to data translation', in: Information Systems, 4, 1979, pp. 35–47

    Google Scholar 

  10. C. Beeri, A.O. Mendelzon, Y. Sagiv, J.D. Ullman: ‘Equivalence of relational database schemes', in: SIAM Journ. of Computing, 10, 1981, pp. 352–370

    Google Scholar 

  11. M. Casanova, R. Fagin, C.H. Papadimitiou: ‘Inclusion dependencies and their interaction with functional dependencies', in: ACM Symp. on Princ. of Database Systems, 1, 1982, pp. 171–176

    Google Scholar 

  12. A.K. Chandra, D. Harel: ‘Computable queries for relational data bases', in: Journ. of Computer and System Sciences, 21, 1980, pp. 156–178

    Google Scholar 

  13. A.K. Chandra, H.R. Lewis, J.A. Makowsky: ‘Embedded implicational dependencies and their inference problem', in: ACM Symp. on Theory of Computing, 13, 1981, pp. 342–354

    Google Scholar 

  14. E.F. Codd: ‘Further normalizations on data base relational model', in: Data Base Systems (R. Rustin ed.), Prentice-Hall, Englewood Cliffs, 1972, pp. 33–64

    Google Scholar 

  15. M.A. Casanova, V.M.P. Vidal: ‘Towards a sound view integration methodology', in: ACM Symp. on Princ. of Database Systems, 2, 1983, pp. 36–47

    Google Scholar 

  16. B. Dreben, W.D. Goldfarb: ‘The decision problem: solvable classes of quantificational formulas', Addison-Wesley Publishing Company, Reading, 1979

    Google Scholar 

  17. R.Fagin, M.Y.Vardi: ‘The theory of data dependencies — a survey', IBM Research Report 4321, San Jose, 1984

    Google Scholar 

  18. W.C. Mc Gee: ‘A contribution to the study of data equivalence', in: Database Management (J.W. Klimbie etc. ed.), Cargese, Amsterdam, 1974, pp. 123–148

    Google Scholar 

  19. J. Grant, B.E. Jacobs: ‘On the family of generalized dependency constraints', in: Journ. of the ACM, 29, 1982, pp. 986–997

    Google Scholar 

  20. J. Graham, A.O. Mendelzon: ‘Strong equivalence of relational expressions under dependencies', in: Information Processing Letters, 14, 1982, pp. 57–62

    Google Scholar 

  21. H. Gallaire, J. Minker, J.M. Nicolas: ‘Logic and databases: a deductive approach', in: ACM Computing Surveys, 16, 1984, pp. 153–185

    Google Scholar 

  22. M.H. Graham, M.Y. Vardi: ‘On the complexity and axiomatizability of consistent database states', in: Proc. ACM Symp. on Princ. of Database Systems, 3, 1984, pp. 281–289

    Google Scholar 

  23. R. Hull: ‘Relative information capacity of simple relational database schemata', Techn. Rep. 84-300, Comp. Science Department, Univ. South. Calif., Los Angeles, 1984

    Google Scholar 

  24. R. Hull: ‘Relative information capacity of simple relational database schemata', in: Proc. ACM Symp. on Princ. of Database Systems, 3, 1984, pp. 97–109

    Google Scholar 

  25. T.Imielinski, W.Lipski: ‘A technique for translating states between database schemata', in: ACM Int. Conf. on Management of data, 1982, pp. 61–68

    Google Scholar 

  26. T. Imielinski, W. Lipski: ‘On the undecidability of equivalence problems for relational expressions', in: Advances in Data Base Theory, 2, 1985, pp. 393–409

    Google Scholar 

  27. T. Imielinski, N. Spyratos: ‘On lossless transformation of database states not necessarily satisfying universal instance assumption', in: Proc. ACM Symp. on Princ. of Database Systems, 3, 1984, pp. 258–265

    Google Scholar 

  28. I. Kobayashi: ‘Losslessness and semantic correctness of database scheme transformation: another look of schema equivalence', in: Information Systems, 11, 1986, pp. 41–59

    Google Scholar 

  29. P.Kandzia, H.J.Klein: ‘On the equivalence of relational data bases in connection with normalization', Techn. Rep. 7901, Univ. Kiel, 1979

    Google Scholar 

  30. B.E. Jacobs, A.R. Aronson, A.C. Klug: ‘On interpretations of relational languages and solutions to the implied constraint problem', in: ACM Transactions on Database Systems, 7, 1982, pp. 291–315

    Google Scholar 

  31. P.C. Kanellakis, S.S. Cosmodakis, M.Y. Vardi: ‘Unary inclusion dependencies have polynomial time inference problem', in: Proc. ACM Symp. Theory of Computing, 15, 1983, pp. 264–277

    Google Scholar 

  32. A. Klug: ‘Calculating constraints on relational expressions', in: ACM Transactions on Database Systems, 5, 1980, pp. 260–290

    Google Scholar 

  33. J.C. Mitchell: ‘The implication problem for functional and inclusion dependencies', in: Information and Control, 56, 1983, pp. 154–173

    Google Scholar 

  34. R. Reiter: ‘Equality and domain closure on first — order databases', in: Journ. of the ACM, 27, 1980, pp. 235–249

    Google Scholar 

  35. J. Rissanen: ‘On the equivalence of database schemes', in: Proc. ACM Symp. Princ. of Database Systems, 1, 1982, pp. 23–26

    Google Scholar 

  36. M.K.Solomon: ‘Undecidability of the equivalence problem for relational expressions', in: Bell Lab. Memo

    Google Scholar 

  37. W. Sierpinski: ‘Cardinal and ordinal numbers', PWN Polish Scientific Publishers, Warschau, 1965

    Google Scholar 

  38. Y. Sagiv, M. Yannakakis: ‘Equivalence among relational expressions', in: Proc. ACM Int. Conf. on Very Large Data Bases, 4, 1978; pp. 535–548

    Google Scholar 

  39. J.D. Ullman: ‘Principle of Database Systems', Computer Science Press, Rockville, 1982

    Google Scholar 

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J. Biskup J. Demetrovics J. Paredaens B. Thalheim

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© 1988 Springer-Verlag Berlin Heidelberg

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Biskup, J., Räsch, U. (1988). The equivalence problem for relational database schemes. In: Biskup, J., Demetrovics, J., Paredaens, J., Thalheim, B. (eds) MFDBS 87. MFDBS 1987. Lecture Notes in Computer Science, vol 305. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-19121-6_4

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  • DOI: https://doi.org/10.1007/3-540-19121-6_4

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  • Online ISBN: 978-3-540-39124-1

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