LIPIcs - Leibniz International Proceedings in Informatics. 23rd International Conference on Rewriting Techniques and Applications (RTA\u2712)
Doi
Abstract
We present a term rewriting system to solve a class of open problems that are generalisations of Kuratowski\u27s closure-complement theorem. The problems are concerned with finding the number of distinct sets that can be obtained by applying combinations of axiomatically defined set operators. While the original problem considers only closure and complement of a topological space as operators, it can be generalised by adding operators and varying axiomatisation. We model these axioms as rewrite rules and construct a rewriting system that allows us to close some so far open variants of Kuratowski\u27s problem by analysing several million inference steps on a typical personal computer
