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See detailMultidimensional generalized automatic sequences and shape-symmetric morphic words
Charlier, Emilie ULg; Kärki, Tomi; Rigo, Michel ULg

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 ▲]

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See detailLattice of subalgebras in the finitely generated varieties of MV-algebras
Teheux, Bruno ULg

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 ▲]

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See detailDecidability questions related to abstract numeration systems
Honkala, Juha; Rigo, Michel ULg

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 ▲]

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See detailConstruction of regular languages and recognizability of polynomials
Rigo, Michel ULg

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 ▲]

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