ENUMERATION AND DECIDABLE PROPERTIES OF AUTOMATIC SEQUENCES

We show that various aspects of k-automatic sequences — such as having an unbordered factor of length n — are both decidable and effectively enumerable. As a consequence it follows that many related sequences are either k-automatic or k-regular. These include many sequences previously studied in the...

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Bibliographic Details
Published in:International journal of foundations of computer science 2012-08, Vol.23 (5), p.1035-1066
Main Authors: CHARLIER, ÉMILIE, RAMPERSAD, NARAD, SHALLIT, JEFFREY
Format: Article
Language:English
Subjects:
Automatic sequence
decidability
Enumeration
Foundations
Mathematical analysis
Mathematical models
Mathematics
Mathématiques
Physical, chemical, mathematical & earth Sciences
Physique, chimie, mathématiques & sciences de la terre
Regular sequence
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Summary:We show that various aspects of k-automatic sequences — such as having an unbordered factor of length n — are both decidable and effectively enumerable. As a consequence it follows that many related sequences are either k-automatic or k-regular. These include many sequences previously studied in the literature, such as the recurrence function, the appearance function, and the repetitivity index. We also give some new characterizations of the class of k-regular sequences. Many results extend to other sequences defined in terms of Pisot numeration systems.
ISSN:0129-0541
1793-6373
DOI:10.1142/S0129054112400448