Conjectures and refutations in database design and dependency theory
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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