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Maximal bifix decoding ; ; et al in Discrete Mathematics (2015), 338(5), 725742 Detailed reference viewed: 16 (5 ULg)Multidimensional generalized automatic sequences and shape-symmetric morphic words Charlier, Emilie ; ; Rigo, Michel in Discrete Mathematics (2010), 310 An infinite word is S-automatic 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 numeration system S. In this paper, we consider an ... [more ▼] An infinite word is S-automatic 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 numeration system S. In this paper, we consider an analogous definition in a multidimensional setting and study its relation to the shapesymmetric infinite words introduced by Arnaud Maes. More precisely, for d>1, we show that a multidimensional infinite word x over a finite alphabet is S-automatic 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 shape-symmetric infinite word. [less ▲] Detailed reference viewed: 59 (16 ULg)Lattice of subalgebras in the finitely generated varieties of MV-algebras Teheux, Bruno in Discrete Mathematics (2007), 307(17-18), 2261-2275 In this paper, we use the theory of natural duality to study subalgebra lattices in the finitely generated varieties of MV-algebras, With this tool, we obtain the dual atomicity of these lattices, and ... [more ▼] In this paper, we use the theory of natural duality to study subalgebra lattices in the finitely generated varieties of MV-algebras, With this tool, we obtain the dual atomicity of these lattices, and characterize the members of these varieties in which every subalgebra is an intersection of maximal subalgebras. Then, we determine the algebras that have a modular or distributive lattice of subalgebras. [less ▲] Detailed reference viewed: 42 (8 ULg)Decidability questions related to abstract numeration systems ; Rigo, Michel in Discrete Mathematics (2004), 285(1-3), 329-333 We show that some decidability questions concerning recognizable sets of integers for abstract numeration systems are equivalent to classical problems related to HD0L systems. It turns out that these ... [more ▼] We show that some decidability questions concerning recognizable sets of integers for abstract numeration systems are equivalent to classical problems related to HD0L systems. It turns out that these problems are decidable when the sets of representations of the integers are slender regular languages. (C) 2004 Elsevier B.V. All rights reserved. [less ▲] Detailed reference viewed: 27 (0 ULg)Construction of regular languages and recognizability of polynomials Rigo, Michel in Discrete Mathematics (2002), 254(1-3), 485-496 A generalization of numeration systems in which NI is recognizable by finite automata can be obtained by describing a lexicographically ordered infinite regular language. We show that if P is an element ... [more ▼] A generalization of numeration systems in which NI is recognizable by finite automata can be obtained by describing a lexicographically ordered infinite regular language. We show that if P is an element of Q[x] is a polynomial such that P(N) subset of N then there exists a numeration system in which the set of representations of P(N) is regular. The main issue is to construct a regular language with a complexity function equals to P(n + 1) - P(n) for n large enough. (C) 2002 Elsevier Science B.V. All rights reserved. [less ▲] Detailed reference viewed: 16 (5 ULg) |
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