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.
O. Al-Hassani, Q. Mahesar, C. Sacerdoti Coen, V. Sorge (2012). A Term Rewriting System for Kuratowski's Closure-Complement Problem. DAGSTUHL : Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik [10.4230/LIPIcs.RTA.2012.38].
A Term Rewriting System for Kuratowski's Closure-Complement Problem
SACERDOTI COEN, CLAUDIO;
2012
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
