Book ChapterDOI
A New Approach to the Paperfolding Sequences
Daniel Goc,Daniel Goc,Hamoon Mousavi,Hamoon Mousavi,Luke Schaeffer,Luke Schaeffer,Jeffrey Shallit +6 more
- pp 34-43
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TLDR
This paper shows how to re-derive known results about the paperfolding sequences, and obtain new ones, using a new approach using a decision method and some machine computation.Abstract:
In this paper we show how to re-derive known results about the paperfolding sequences, and obtain new ones, using a new approach using a decision method and some machine computation. We also obtain exact expressions for the recurrence and appearance function of the paperfolding sequences, and solve an open problem of Rampersad about factors shared in common between two different paperfolding sequences.read more
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Automatic Theorem Proving in Walnut.
TL;DR: Walnut is a software package that implements a mechanical decision procedure for deciding certain combinatorial properties of some special words referred to as automatic words or automatic sequences.
Journal ArticleDOI
Pseudoperiodic Words and a Question of Shevelev
TL;DR: In this article , the authors generalize the notion of periodicity in sequences to a new kind of pseudoperiodicity, which they call Pseudo-periodicity, and introduce a new notion of pseudobased periodicity.
Journal ArticleDOI
The First-Order Theory of Binary Overlap-Free Words is Decidable
Luke Schaeffer,Jeffrey Shallit +1 more
TL;DR: It is shown that the first-order logical theory of the binary overlap-free words and the α -free words for rational α, 2 < α ≤ 7 / 3, is decidable, and many results previously obtained through tedious case-based proofs can now be proved “automatically”, using a decision procedure.
The appearance function for paper-folding words
TL;DR: In this paper , the authors provide a complete characterisation of the appearance function for paperfolding sequences for factors of any length and make use of the software package Walnut to establish these results.
References
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Journal ArticleDOI
Uniform tag sequences
TL;DR: Structural properties, local and asymptotic, of members of a class of simple, realtime generable sequences are analyzed.
Journal ArticleDOI
Enumeration and decidable properties of automatic sequences
TL;DR: It is shown that various aspects of k-automatic sequences — such as having an unbordered factor of length n — are both decidable and effectively enumerable, and many related sequences are either k- automatic or k-regular.
Journal ArticleDOI
Periodicity, repetitions, and orbits of an automatic sequence
TL;DR: In this paper, the authors revisited a technique of S Lehr on automata and used it to prove old and new results in a simple way, and showed that it is decidable whether a given k-automatic sequence is ultimately periodic.
Posted Content
Periodicity, repetitions, and orbits of an automatic sequence
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.
Journal ArticleDOI
The number of factors in a paperfolding sequence
TL;DR: In this article, it was shown that the number of factors of length k in any paperfolding sequence is equal to 4k once k ≥ 7, where k is the length of the paper.