A Term Rewriting System for Kuratowski's Closure-Complement Problem

Osama Al-Hassani, Quratul-Ain Mahesar, Claudio Sacerdoti Coen, Volker Sorge, Marc Herbstritt
2012 International Conference on Rewriting Techniques and Applications  
We present a term rewriting system to solve a class of open problems that are generalisations of Kuratowski's 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
more » ... xioms as rewrite rules and construct a rewriting system that allows us to close some so far open variants of Kuratowski's problem by analysing several million inference steps on a typical personal computer.
doi:10.4230/lipics.rta.2012.38 dblp:conf/rta/Al-HassaniMCS12 fatcat:rhjegihn6vhajb7wx3sk3phare