Similarity density of the Thue-Morse word with overlap-free infinite binary words
We consider a measure of similarity for infinite words that generalizes the notion of asymptotic or natural density of subsets of natural numbers from number theory. We show that every overlap-free infinite binary word, other than the Thue-Morse word t and its complement t bar, has this measure of s...
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| Format: | Article |
| Language: | English |
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Open Publishing Association
2014-05-01
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| Series: | Electronic Proceedings in Theoretical Computer Science |
| Online Access: | http://arxiv.org/pdf/1405.5605v1 |
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Article |
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doaj-b523681fd4814398b388c7a4d962d1f22020-11-25T00:41:19ZengOpen Publishing AssociationElectronic Proceedings in Theoretical Computer Science2075-21802014-05-01151Proc. AFL 201423124510.4204/EPTCS.151.16:5Similarity density of the Thue-Morse word with overlap-free infinite binary wordsChen Fei Du0Jeffrey Shallit1 University of Waterloo University of Waterloo We consider a measure of similarity for infinite words that generalizes the notion of asymptotic or natural density of subsets of natural numbers from number theory. We show that every overlap-free infinite binary word, other than the Thue-Morse word t and its complement t bar, has this measure of similarity with t between 1/4 and 3/4. This is a partial generalization of a classical 1927 result of Mahler.http://arxiv.org/pdf/1405.5605v1 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Chen Fei Du Jeffrey Shallit |
| spellingShingle |
Chen Fei Du Jeffrey Shallit Similarity density of the Thue-Morse word with overlap-free infinite binary words Electronic Proceedings in Theoretical Computer Science |
| author_facet |
Chen Fei Du Jeffrey Shallit |
| author_sort |
Chen Fei Du |
| title |
Similarity density of the Thue-Morse word with overlap-free infinite binary words |
| title_short |
Similarity density of the Thue-Morse word with overlap-free infinite binary words |
| title_full |
Similarity density of the Thue-Morse word with overlap-free infinite binary words |
| title_fullStr |
Similarity density of the Thue-Morse word with overlap-free infinite binary words |
| title_full_unstemmed |
Similarity density of the Thue-Morse word with overlap-free infinite binary words |
| title_sort |
similarity density of the thue-morse word with overlap-free infinite binary words |
| publisher |
Open Publishing Association |
| series |
Electronic Proceedings in Theoretical Computer Science |
| issn |
2075-2180 |
| publishDate |
2014-05-01 |
| description |
We consider a measure of similarity for infinite words that generalizes the notion of asymptotic or natural density of subsets of natural numbers from number theory. We show that every overlap-free infinite binary word, other than the Thue-Morse word t and its complement t bar, has this measure of similarity with t between 1/4 and 3/4. This is a partial generalization of a classical 1927 result of Mahler. |
| url |
http://arxiv.org/pdf/1405.5605v1 |
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AT chenfeidu similaritydensityofthethuemorsewordwithoverlapfreeinfinitebinarywords AT jeffreyshallit similaritydensityofthethuemorsewordwithoverlapfreeinfinitebinarywords |
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