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Ambiguity for referential integrity is undecidable

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1034))

Abstract

SQL has grown to be the language for relational database systems. One vital element of the relational model is referential integrity. This type of integrity constraints is now included in the new SQL2 standard [11] with capabilities to react on violations of specified integrity constraints. These reactions may lead to indeterminism with respect to the outcome of a user operation which is also known from the usage of rules or triggers. In the database context, however, such ambiguities are undesirable. Hence, for each submitted operation one must check whether or not an ambiguity occurs, and in the former case rollback the operation. Since such checks are time consuming, one might consider performing them only for schemas which bear the risk of an indeterminism. This paper shows that it is undecidable whether or not a schema may have an instance leading to ambiguities. Therefore, unnecessary checks cannot be avoided in general.

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References

  1. A. Aiken, J. M. Hellerstein, and J. Widom. Static Analysis Techniques for Predicting the Behavior of Active Database Rules. ACM TODS, 20(1):3–41, March 1995.

    Google Scholar 

  2. A. Aiken, J. Widom, and J. M. Hellerstein. Behavior of Database Production Rules: Termination, Confluence, and Observable Determinism. ACM SIGMOD Record, 20(2):59–68, June 1992.

    Google Scholar 

  3. A.K. Chandra and M. Y. Vardi. The Implication Problem for Functional and Inclusion Dependencies is Undecidable. ACM SIAM, 14(3):671–677, 1985.

    Google Scholar 

  4. E. F. Codd. A Relational Model of Data for Large Shared Databases. Communication of the ACM, 13(6):377–387, 1970.

    Google Scholar 

  5. C. J. Date. Referential Integrity. In Proceedings of the VLDB'81, pages 9–35. IEEE, March 1981.

    Google Scholar 

  6. C. J. Date. A Guide to THE SQL STANDARD. Addision-Wesley, New York, 1988.

    Google Scholar 

  7. C. J. Date. Relational Databases: Selected Writings 1985–1989. Addision-Wesley, New York, 1990.

    Google Scholar 

  8. K. P. Eswaran. Specification, Implementation and Interactions of a Trigger Subsystem in a Integrated Database System. IBM Research Report RJ-1820(26414), IBM Almaden Research Center, IBM Research Laboratory, San Jose, California 95193, 1976.

    Google Scholar 

  9. M. M. Hammer and D. J. McLeod. Semantic Integrity in a Relational Data Base System. In Proceedings of the VLDB'75, pages 25–47, 1975.

    Google Scholar 

  10. T. Härder and J. Reinert. Access Path Support for Referential Integrity in SQL2. Research Report, Fachbereich Informatik, Universität Kaiserslautern, Postfach 3049, D-W 6750 Kaiserslautern, Germany, 1993.

    Google Scholar 

  11. ISO/IEC JTC1/SC21. Information Technology — Database Languages — SQL2. ANSI, American National Standards Institute, 1430 Broadway, New York, NY 10018, July 1992.

    Google Scholar 

  12. ISO/IEC JTC1/SC21/WG3. ISO/ANSI working draft Database Languages — SQL3. ANSI, American National Standards Institute, 1430 Broadway, New York, NY 10018, February 1993.

    Google Scholar 

  13. V. M. Markowitz. Referential Integrity Revisited: An Object-Oriented Perspective. In Proceedings of the VLDB'90, Australia, pages 9–35, 1990.

    Google Scholar 

  14. V. M. Markowitz. Safe Referential Integrity Structures. In Proceedings of the VLDB'91, Barcelona, Spain, 1991.

    Google Scholar 

  15. V. M. Markowitz. Safe Referential Integrity and Null Constraints in Relational Databases. Information Systems, 19(4):359–378, 1994.

    Google Scholar 

  16. G. Moerkotte. Inkonsitenzen in deduktiven Datenbanken. Springer-Verlag, Heidelberg, 1990. in German.

    Google Scholar 

  17. J. Reinert. Ensuring Referential Integrity in SQL2 and SQL3. Research Report, University of Kaiserslautern, 1992.

    Google Scholar 

  18. J. Widom and S. J. Finkelstein. Syntax and Semantics for Set-Oriented Production Rules in Relational Database Systems. IBM Research Report 6880, IBM Almaden Research Center, IBM Research Laboratory, San Jose, California 95193, 1989.

    Google Scholar 

  19. J. Widom and S. J. Finkelstein. Set-Oriented Production Rules in Relational Database Systems. ACM SIGMOD Record, 19(2):259–270, June 1990.

    Google Scholar 

  20. Y. Zhou and M. Hsu. A Theory for Rule Triggering Systems. In Proceedings of the EDBT 92, LNCS 416, pages 407–421. Springer-Verlag, Berlin, March 1990.

    Google Scholar 

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Gabriel Kuper Mark Wallace

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© 1996 Springer-Verlag Berlin Heidelberg

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Reinert, J. (1996). Ambiguity for referential integrity is undecidable. In: Kuper, G., Wallace, M. (eds) Constraint Databases and Application. CDB 1995. Lecture Notes in Computer Science, vol 1034. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60794-3_18

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  • DOI: https://doi.org/10.1007/3-540-60794-3_18

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60794-6

  • Online ISBN: 978-3-540-49456-0

  • eBook Packages: Springer Book Archive

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