Enumeration and decidable properties of automatic sequences

Authors:
Émilie Charlier;Narad Rampersad;Jeffrey Shallit
Affiliations:
University of Waterloo, Waterloo, ON, Canada;Department of Mathematics, University of Liège, Liège, Belgium;University of Waterloo, Waterloo, ON, Canada
Venue:
DLT'11 Proceedings of the 15th international conference on Developments in language theory
Year:
2011

Citing 12
Cited 1

The ring of k-regular sequences

Theoretical Computer Science
Separators in infinite words generated by morphisms

Theoretical Computer Science
Bertrand numeration systems and recognizability

Theoretical Computer Science - Special issue: Latin American theoretical informatics
Palindrome complexity

Theoretical Computer Science
Automatic Sequences: Theory, Applications, Generalizations

Automatic Sequences: Theory, Applications, Generalizations
The ring of k-regular sequences, II

Theoretical Computer Science - WORDS
A Polynomial Time Presburger Criterion and Synthesis for Number Decision Diagrams

LICS '05 Proceedings of the 20th Annual IEEE Symposium on Logic in Computer Science
Every real number greater than 1 is a critical exponent

Theoretical Computer Science
Periodicity, repetitions, and orbits of an automatic sequence

Theoretical Computer Science
Elements of Automata Theory

Elements of Automata Theory
On factors of synchronized sequences

Theoretical Computer Science
On the periodicity of morphic words

DLT'10 Proceedings of the 14th international conference on Developments in language theory

Automatic theorem-proving in combinatorics on words

CIAA'12 Proceedings of the 17th international conference on Implementation and Application of Automata

Quantified Score

Hi-index	0.00

Visualization

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.