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Logic and precognizable sets of integers
 Bull. Belg. Math. Soc
, 1994
"... We survey the properties of sets of integers recognizable by automata when they are written in pary expansions. We focus on Cobham’s theorem which characterizes the sets recognizable in different bases p and on its generalization to N m due to Semenov. We detail the remarkable proof recently given ..."
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Cited by 68 (4 self)
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We survey the properties of sets of integers recognizable by automata when they are written in pary expansions. We focus on Cobham’s theorem which characterizes the sets recognizable in different bases p and on its generalization to N m due to Semenov. We detail the remarkable proof recently given by Muchnik for the theorem of CobhamSemenov, the original proof being published in Russian. 1
Extensions and restrictions of Wythoff’s game preserving its P positions
 Journal of Combinatorial Theory, Series A
"... Abstract. We consider extensions and restrictions of Wythoff’s game having exactly the same set of P positions as the original game. No strict subset of rules give the same set of P positions. On the other hand, we characterize all moves that can be adjoined while preserving the original set of P po ..."
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Cited by 9 (5 self)
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Abstract. We consider extensions and restrictions of Wythoff’s game having exactly the same set of P positions as the original game. No strict subset of rules give the same set of P positions. On the other hand, we characterize all moves that can be adjoined while preserving the original set of P positions. Testing if a move belongs to such an extended set of rules is shown to be doable in polynomial time. Many arguments rely on the infinite Fibonacci word, automatic sequences and the corresponding number system. With these tools, we provide new twodimensional morphisms generating an infinite picture encoding respectively P positions of Wythoff’s game and moves that can be adjoined. 1.
Local Configurations in a Discrete Plane.
 Bull. Belg. Math. Soc
, 1999
"... : We study the number of local configurations in a discrete plane. We convert this problem into a computation of a double sequence complexity. We compute the number C(n; m) of distinct n \Theta m patterns appearing in a discrete plane. We show that C(n; m) = nm for all n and m positive integers. Th ..."
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Cited by 7 (4 self)
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: We study the number of local configurations in a discrete plane. We convert this problem into a computation of a double sequence complexity. We compute the number C(n; m) of distinct n \Theta m patterns appearing in a discrete plane. We show that C(n; m) = nm for all n and m positive integers. The coding of this sequence by a Z 2 action on the unidimensional torus gives information about the structure of a discrete plane. Furthermore, this sequence is a generalized Rote sequence with complexity P (n; m) = 2nm for all n and m positive integers and with a symmetric complementary language for rectangular words. Keywords: Discrete planes, double sequence complexity, plane partitions, symmetric complementary language, generalization of Rote and Sturmian sequences. 1 Introduction In this article, we use the notion of complexity for a double sequence to study local configurations in a discrete plane. The complexity function p(n) for a sequence in a finite alphabet is defined from N to...
ABOUT FREQUENCIES OF LETTERS IN GENERALIZED AUTOMATIC SEQUENCES
"... Abstract. We present some asymptotic results about the frequency of a letter appearing in a generalized unidimensional automatic sequence. Next, we study multidimensional generalized automatic sequences and the corresponding frequencies. 1. ..."
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Cited by 2 (2 self)
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Abstract. We present some asymptotic results about the frequency of a letter appearing in a generalized unidimensional automatic sequence. Next, we study multidimensional generalized automatic sequences and the corresponding frequencies. 1.
Discrete Planes, Z²Actions, JacobiPerron Algorithm and Substitutions
 ANN. INST. FOURIER (GRENOBLE
, 2001
"... We introduce twodimensional substitutions generating twodimensional sequences related to discrete approximations of irrational planes. These twodimensional substitutions are produced by the classical JacobiPerron continued fraction algorithm, by the way of induction of a Z²action by rotations ..."
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We introduce twodimensional substitutions generating twodimensional sequences related to discrete approximations of irrational planes. These twodimensional substitutions are produced by the classical JacobiPerron continued fraction algorithm, by the way of induction of a Z²action by rotations on the circle. This gives a new geometric interpretation of the JacobiPerron algorithm, as a map operating on the parameter space of Z²actions by rotations.
Contents lists available at ScienceDirect Discrete Mathematics
"... journal homepage: www.elsevier.com/locate/disc Multidimensional generalized automatic sequences and ..."
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journal homepage: www.elsevier.com/locate/disc Multidimensional generalized automatic sequences and
MULTIDIMENSIONAL GENERALIZED AUTOMATIC SEQUENCES AND SHAPESYMMETRIC MORPHIC WORDS
, 907
"... Abstract. An infinite word is Sautomatic if, for all n ≥ 0, its (n+1)st letter is the output of a deterministic automaton fed with the representation of n in the considered numeration system S. In this paper, we consider an analogous definition in a multidimensional setting and study the relationsh ..."
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Abstract. An infinite word is Sautomatic if, for all n ≥ 0, its (n+1)st letter is the output of a deterministic automaton fed with the representation of n in the considered numeration system S. In this paper, we consider an analogous definition in a multidimensional setting and study the relationship with the shapesymmetric infinite words as introduced by Arnaud Maes. Precisely, for d ≥ 2, we show that a multidimensional infinite word x: N d → Σ over a finite alphabet Σ is Sautomatic for some abstract numeration system S built on a regular language containing the empty word if and only if x is the image by a coding of a shapesymmetric infinite word. 1.
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"... This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal noncommercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or sel ..."
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This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal noncommercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier’s archiving and manuscript policies are encouraged to visit: