Morphisms and almost-periodicity
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TL;DR: A criterion, using oriented graphs, to decide whether an infinite word generated as fixed point of an expanding morphism on a finite alphabet is (effectively) almost-periodic is given.
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About: This article is published in Discrete Applied Mathematics. The article was published on 01 Sep 1998. and is currently open access. The article focuses on the topics: Unary operation & Quantifier elimination.
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Citations
Combinatorics, Automata and Number Theory
Valrie Berth,Michel Rigo +1 more
- 30 Sep 2010
TL;DR: In this article, the authors present recent trends arising from the fruitful interaction between the themes of combinatorics on words, automata and formal language theory, and number theory and reveal some of the exciting and important relationships that exist between these different fields.
Decidability of uniform recurrence of morphic sequences
TL;DR: It is proved that the uniform recurrence of morphic sequences is decidable and the number of derived sequences of uniformly recurrent morphic Sequence is bounded, and it is obtained that uniformly recurrent Morphic sequences are primitive substitutive sequences.
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•Posted Content
Decidability of uniform recurrence of morphic sequences
TL;DR: In this paper, it was shown that the uniform recurrence of morphic sequences is decidable and that the number of derived sequences of a uniformly recurrent morphic sequence is bounded.
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On Cobham’s theorem
Fabien Durand,Michel Rigo +1 more
- 13 Sep 2021
TL;DR: In this paper, the representation of non-negative integers in a given numeration system is studied and the main role of such a system is to replace numbers or more generally sets of numbers by their corresponding representations, i.e. by words or languages.
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More on morphisms and almost-periodicity
TL;DR: It is shown that a word W obtained as fixed point of a morphism ϕ is almost-periodic if and only if either no growing factor occurs infinitely often in W or the set of non-growing factors of W is finite.
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References
On certain extensions of the arithmetic of addition of natural numbers
TL;DR: In this article, the expressibility and decidability of elementary theories obtained by extending the arithmetic of order and arithmetic of addition of natural numbers are studied. But the problems of expressibility of these theories are not studied.
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More on morphisms and almost-periodicity
TL;DR: It is shown that a word W obtained as fixed point of a morphism ϕ is almost-periodic if and only if either no growing factor occurs infinitely often in W or the set of non-growing factors of W is finite.
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•Proceedings Article
More on Morphisms and Almost-Periodicity.
Arnaud Maes
- 01 Jan 1998
TL;DR: In this article, it was shown that a word W obtained as fixed point of a morphism ϕ is almost-periodic if and only if either no growing factor occurs infinitely often in W or if the set of non-growing factors of W is finite and the graph of the incidence relation induced by the morphism on the Λ+2 factors is strongly connected.
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LOGIC AND p-RECOGNIZABLE SETS OF INTEGERS
TL;DR: Cobham’s theorem is focused on which characterizes the sets recognizable in dierent bases p and on its generalization to N m due to Semenov.