Advertisement

Conjectures and refutations in database design and dependency theory

  • Jyrki Nummenmaa
  • Peter Thanisch
Dependencies
Part of the Lecture Notes in Computer Science book series (LNCS, volume 470)

Abstract

In the related fields of database design theory and dependency theory, when a conjecture is refuted or an algorithm is shown to be incorrect, it is often the case that the counterexample found is quite small. We contend that this is because the conjectures and algorithms refer to structures that can only interact with each other in a limited number of ways. On the basis of this contention, we have implemented software that can find specific examples of such interactions and, consequently, can attempt to generate counterexamples to conjectures and methods. We are currently developing the software so that it can use the generated counterexamples to assist in conjecture refinement.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [Ang87]
    D. Angluin, Learning regular sets from queries and counterexamples, Information and Computation 75 (1987), 87–106.CrossRefGoogle Scholar
  2. [Atk88]
    J. Atkins, A Note on Minimal Covers, Sigmod Record, 17, No 4, December 1988, 16–21.Google Scholar
  3. [BFMY83]
    C. Beeri and R. Fagin, D. Maier and M. Yannakakis, On the desirability of acyclic database schemes, J. ACM 30 (1983), 479–513.CrossRefGoogle Scholar
  4. [Bled82]
    W. Bledsoe, Using Examples to Generate Instantiations for Set Variables, Report ATP-67, University of Texas at Austin, Dept. of Mathematics and Computer Science.Google Scholar
  5. [Fag83]
    R. Fagin, Degrees of acyclicity for hypergraphs and relational database schemes, J. ACM 30 (1983), 514–550.Google Scholar
  6. [Mai83]
    D. Maier, The theory of relational databases, Computer Science Press, Rockville, Maryland, 1983.Google Scholar
  7. [NuTh90]
    J. Nummenmaa and P. Thanisch, Yet another note on minimal covers, to appear in SIGMOD Record.Google Scholar
  8. [Rob65]
    J. Robinson, A machine-oriented logic based on the resolution principle, J. ACM 12 (1965), 23–41.CrossRefGoogle Scholar
  9. [Var88]
    M.Y. Vardi, Fundamentals of dependency theory. In: Trends in Theoretical Computer Science, E. Börger, ed. Computer Science Press, Rockville, Maryland, 1988, 171–224.Google Scholar
  10. [Win82]
    S. Winker, Generation and verification of finite models and counterexamples using an automated theorem prover answering two open questions, J. ACM 29 (1982), 273–284.Google Scholar
  11. [YuÖz86]
    L-Y Yuan and Z.M. Özsoyoslu, Unifying functional and multivalued dependencies for relational database design, 5th ACM Symposium on Principles of Database Systems, 1986, 183–190.Google Scholar
  12. [YuÖz87]
    L-Y Yuan and Z.M. Özsoyoslu, Logical design of relational database schemes, 6th ACM Symposium on Principles of Database Systems, 1987, 38–47.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • Jyrki Nummenmaa
    • 1
  • Peter Thanisch
    • 2
  1. 1.Department of Computer ScienceUniversity of TampereTampereFinland
  2. 2.Department of Computer ScienceUniversity of EdinburghEdinburghScotland

Personalised recommendations