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

Authors: Osama Al-Hassani, Quratul-ain Mahesar, Claudio Sacerdoti Coen, and Volker Sorge

Published in: LIPIcs, Volume 15, 23rd International Conference on Rewriting Techniques and Applications (RTA'12) (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.

Cite as

Osama Al-Hassani, Quratul-ain Mahesar, Claudio Sacerdoti Coen, and Volker Sorge. A Term Rewriting System for Kuratowski's Closure-Complement Problem. In 23rd International Conference on Rewriting Techniques and Applications (RTA'12). Leibniz International Proceedings in Informatics (LIPIcs), Volume 15, pp. 38-52, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)


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@InProceedings{alhassani_et_al:LIPIcs.RTA.2012.38,
  author =	{Al-Hassani, Osama and Mahesar, Quratul-ain and Sacerdoti Coen, Claudio and Sorge, Volker},
  title =	{{A Term Rewriting System for Kuratowski's Closure-Complement Problem}},
  booktitle =	{23rd International Conference on Rewriting Techniques and Applications (RTA'12)},
  pages =	{38--52},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-38-5},
  ISSN =	{1868-8969},
  year =	{2012},
  volume =	{15},
  editor =	{Tiwari, Ashish},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.RTA.2012.38},
  URN =		{urn:nbn:de:0030-drops-34838},
  doi =		{10.4230/LIPIcs.RTA.2012.38},
  annote =	{Keywords: Kuratowski's closure-complement problem, Rewriting system}
}
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