eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2012-05-29
38
52
10.4230/LIPIcs.RTA.2012.38
article
A Term Rewriting System for Kuratowski's Closure-Complement Problem
Al-Hassani, Osama
Mahesar, Quratul-ain
Sacerdoti Coen, Claudio
Sorge, Volker
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 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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol015-rta2012/v20120508-organizer-final/LIPIcs.RTA.2012.38/LIPIcs.RTA.2012.38.pdf
Kuratowski's closure-complement problem
Rewriting system