By using the universal Diophantine representation of recursively enumerable sets of positive integers due to Matiyasevich we construct a Z-rational series r over a binary alphabet X which has a maximal image complexity in the sense that all recursively enumerable sets of positive integers are obtained as the sets of positive coefficients of the series w-1r where w ∈ X∗. As a consequence we obtain various undecidability results for Z-rational series
This paper concerns power series of an arithmetic nature that arise in the analysis of divide-and-co...
We prove that, for any fixed d, there is a polynomial time algorithm for computing the generating fu...
AbstractAll solutions in positive integers x, y z of the diophantine equation x1m + y1n = z1r are de...
By using the universal Diophantine representation of recursively enumerable sets of positive integer...
AbstractWe show that the problem of determining if a given integer linear recurrent sequence has a z...
We consider the decidability and complexity of the Ultimate Positivity Problem, which asks whether a...
Abstract. We consider the decidability and complexity of the Ultimate Positivity Problem, which asks...
We show that the problem of determining if a given integer linear recurrent sequence has a zero-a pr...
Consider partial maps ∑* → $\mathbb R$ with a rational domain. We show that two families of such ser...
AbstractAnswering a question of Liardet, we prove that if 1,α1,α2,…,αt are real numbers linearly ind...
We study the representation of the solutions of a polynomial system by triangular sets, and concentr...
AbstractThe main result of this article is the Representation Theorem which characterizes families o...
AbstractAlgorithms can be used to prove and to discover new theorems. This paper shows how algorithm...
International audienceIn this paper, it is shown that the Hilbert series of a Borel type ideal may b...
We investigate algebraic and arithmetic properties of a class of sequences of sparse polynomials th...
This paper concerns power series of an arithmetic nature that arise in the analysis of divide-and-co...
We prove that, for any fixed d, there is a polynomial time algorithm for computing the generating fu...
AbstractAll solutions in positive integers x, y z of the diophantine equation x1m + y1n = z1r are de...
By using the universal Diophantine representation of recursively enumerable sets of positive integer...
AbstractWe show that the problem of determining if a given integer linear recurrent sequence has a z...
We consider the decidability and complexity of the Ultimate Positivity Problem, which asks whether a...
Abstract. We consider the decidability and complexity of the Ultimate Positivity Problem, which asks...
We show that the problem of determining if a given integer linear recurrent sequence has a zero-a pr...
Consider partial maps ∑* → $\mathbb R$ with a rational domain. We show that two families of such ser...
AbstractAnswering a question of Liardet, we prove that if 1,α1,α2,…,αt are real numbers linearly ind...
We study the representation of the solutions of a polynomial system by triangular sets, and concentr...
AbstractThe main result of this article is the Representation Theorem which characterizes families o...
AbstractAlgorithms can be used to prove and to discover new theorems. This paper shows how algorithm...
International audienceIn this paper, it is shown that the Hilbert series of a Borel type ideal may b...
We investigate algebraic and arithmetic properties of a class of sequences of sparse polynomials th...
This paper concerns power series of an arithmetic nature that arise in the analysis of divide-and-co...
We prove that, for any fixed d, there is a polynomial time algorithm for computing the generating fu...
AbstractAll solutions in positive integers x, y z of the diophantine equation x1m + y1n = z1r are de...
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