On the decidability of semigroup freeness∗

Julien Cassaigne; Francois Nicolas

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On the decidability of semigroup freeness

Julien Cassaigne, Francois Nicolas (2012)

RAIRO - Theoretical Informatics and Applications

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This paper deals with the decidability of semigroup freeness. More precisely, the freeness problem over a semigroup is defined as: given a finite subset ⊆ , decide whether each element of has at most one factorization over . To date, the decidabilities of the following two freeness problems have been closely examined. In 1953, Sardinas and Patterson proposed a now famous algorithm for the freeness problem over the free...

On the decidability of semigroup freeness

Julien Cassaigne, Francois Nicolas (2012)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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Transition de dépiégeage élastique de vortex supraconducteurs

Enrick Olive, Nicolas Di Scala, Yves Lansac, Yaouen Fily, Jean-Claude Soret (2012)

ESAIM: Proceedings

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We present 2D numerical simulation results of superconductor vortex lattices driven over a random disorder. The vortex dynamics at the depinning threshold is studied at zero temperature in the case of weak disorder. The dynamics is elastic and the depinning transition is analysed in the framework of a second order phase transition where the velocity response to the driving force behaves like ~ ( − ...

High-frequency limit of the Maxwell-Landau-Lifshitz equations in the diffractive optics regime

LU Yong (2012)

ESAIM: Proceedings

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We study the Maxwell-Landau-Lifshitz system for highly oscillating initial data, with characteristic frequencies (1 ) and amplitude (1), over long time intervals (1 ), in the limit → 0. We show that a nonlinear Schrödinger equation gives a good approximation for the envelope of the solution in the time interval under consideration. This extends previous results of Colin and Lannes [1]. This text is a short version of the article [5].

Substitution systems associated with the dynamical system (𝒜, )

Maria de Fátima Correia, Carlos Ramos, Sandra Vinagre (2012)

ESAIM: Proceedings

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We consider the dynamical system (𝒜, ), where 𝒜 is a class of differential real functions defined on some interval and : 𝒜 → 𝒜 is an operator := , where is a differentiable -modal map. If we consider functions in 𝒜 whose critical values are periodic points for then, we show how to define and characterize a substitution system associated with (𝒜, ...

Regularity of languages defined by formal series with isolated cut point

Alberto Bertoni, Maria Paola Bianchi, Flavi D’Alessandro (2012)

RAIRO - Theoretical Informatics and Applications

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Let = { ∈ | () } be the language recognized by a formal series : → ℝ with isolated cut point . We provide new conditions that guarantee the regularity of the language in the case that is rational or is a Hadamard quotient of rational series. Moreover the decidability property of such conditions is investigated.

Regularity of languages defined by formal series with isolated cut point

Alberto Bertoni, Maria Paola Bianchi, Flavi D’Alessandro (2012)

RAIRO - Theoretical Informatics and Applications

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Equations on partial words

Francine Blanchet-Sadri, D. Dakota Blair, Rebeca V. Lewis (2007)

RAIRO - Theoretical Informatics and Applications

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It is well-known that some of the most basic properties of words, like the commutativity () and the conjugacy (), can be expressed as solutions of word equations. An important problem is to decide whether or not a given equation on words has a solution. For instance, the equation has only periodic solutions in a free monoid, that is, if holds with integers , then there exists a word such that are powers of . This result, which received a lot of attention, was first proved by Lyndon...