Topic
Automatic sequence
About: Automatic sequence is a research topic. Over the lifetime, 133 publications have been published within this topic receiving 2747 citations. The topic is also known as: k-automatic sequence & k-recognizable sequence.
Papers published on a yearly basis
Papers
Book•
1 Jan 2003TL;DR: This chapter discusses automata, automatic sequences, and other models of computation in number theory and algebra, as well as number systems and numeration systems, and some examples of these models are presented.
Abstract: Preface 1. Stringology 2. Number theory and algebra 3. Numeration systems 4. Finite automata and other models of computation 5. Automatic sequences 6. Uniform morphisms and automatic sequences 7. Morphic sequences 8. Frequency of letters 9. Characteristic words 10. Subwords 11. Cobham's theorem 12. Formal power series 13. Automatic real numbers 14. Multidimensional automatic sequences 15. Automaticity 16. k-regular sequences 17. Physics Appendix. Hints, references and solutions for selected exercises Bibliography Index.
1,091 citations
1 Jan 1995
TL;DR: In the following pages the authors discuss infinite sequences defined on a finite alphabet, and more specially those which are generated by finite automata.
Abstract: In the following pages we discuss infinite sequences defined on a finite alphabet, and more specially those which are generated by finite automata. We have divided our paper into seven parts which are more or less self-contained. Needless to say, we feel that the order we propose is the most natural one. References appear at the end of each one of the parts which implies some redundancy.
55 citations
Posted Content•
TL;DR: It is shown that several related quantities, such as the critical exponent, irrationality measure, and recurrence quotient for Sturmian words with slope @a, have automatic continued fraction expansions if @a does, and it is proved that the lexicographically least sequence in the orbit closure of a k-automatic sequence is k- automatic.
Abstract: We revisit a technique of S. Lehr on automata and use it to prove old and new results in a simple way. We give a very simple proof of the 1986 theorem of Honkala that it is decidable whether a given k-automatic sequence is ultimately periodic. We prove that it is decidable whether a given k-automatic sequence is overlap-free (or squareefree, or cubefree, etc.) We prove that the lexicographically least sequence in the orbit closure of a k-automatic sequence is k-automatic, and use this last result to show that several related quantities, such as the critical exponent, irrationality measure, and recurrence quotient for Sturmian words with slope alpha, have automatic continued fraction expansions if alpha does.
54 citations
19 Jul 2011
TL;DR: In this paper, it was shown that many aspects of k-automatic sequences are decidable and effectively enumerable, such as recurrence function, appearance function, and repetitivity index.
Abstract: 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 a new characterization of the class of k-regular sequences. Many results extend to other sequences defined in terms of Pisot numeration systems.
53 citations
TL;DR: Here, the concept of k-automatic sequence for abstract numeration systems on a regular language (instead of systems in base k) is generalized and the first properties of these sequences are studied.
38 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2022 | 2 |
| 2021 | 7 |
| 2020 | 8 |
| 2019 | 3 |
| 2018 | 9 |
| 2017 | 7 |