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.
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References
D. Angluin, Learning regular sets from queries and counterexamples, Information and Computation 75 (1987), 87–106.
J. Atkins, A Note on Minimal Covers, Sigmod Record, 17, No 4, December 1988, 16–21.
C. Beeri and R. Fagin, D. Maier and M. Yannakakis, On the desirability of acyclic database schemes, J. ACM 30 (1983), 479–513.
W. Bledsoe, Using Examples to Generate Instantiations for Set Variables, Report ATP-67, University of Texas at Austin, Dept. of Mathematics and Computer Science.
R. Fagin, Degrees of acyclicity for hypergraphs and relational database schemes, J. ACM 30 (1983), 514–550.
D. Maier, The theory of relational databases, Computer Science Press, Rockville, Maryland, 1983.
J. Nummenmaa and P. Thanisch, Yet another note on minimal covers, to appear in SIGMOD Record.
J. Robinson, A machine-oriented logic based on the resolution principle, J. ACM 12 (1965), 23–41.
M.Y. Vardi, Fundamentals of dependency theory. In: Trends in Theoretical Computer Science, E. Börger, ed. Computer Science Press, Rockville, Maryland, 1988, 171–224.
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.
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.
L-Y Yuan and Z.M. Özsoyoslu, Logical design of relational database schemes, 6th ACM Symposium on Principles of Database Systems, 1987, 38–47.
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© 1990 Springer-Verlag Berlin Heidelberg
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Nummenmaa, J., Thanisch, P. (1990). Conjectures and refutations in database design and dependency theory. In: Abiteboul, S., Kanellakis, P.C. (eds) ICDT '90. ICDT 1990. Lecture Notes in Computer Science, vol 470. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-53507-1_79
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DOI: https://doi.org/10.1007/3-540-53507-1_79
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