Soria-Cousineau, M. Methodes d'analyse pour les constructions combinatoires et les algorithmes. Doctorat es sciences, Universite de Paris{Sud, Orsay, July 1990.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....ne a sequence construction to be supercritical if C = S(A) and A C . Then an adapted singular Boltzmann generator for C produces a random C object of size n O(1) in one trial, with high probability. Proof. The notion and properties of supercriticality in this context are borrowed from Soria [29]. The adapted algorithm does simply as follows: repeat: draw in A according to A(rho) until total size = n; Literally taken, the singular Boltzmann would loop for ever. The isolated polar singularity of C(x) at entails the promised characteristics by virtue of common properties of ....

Soria-Cousineau, M. Methodes d'analyse pour les constructions combinatoires et les algorithmes. Doctorat es sciences, Universite de Paris{Sud, Orsay, July 1990.

....A(x) should cross the value 1 before it becomes singular. The generating function of C and A satisfy C(z) 1= 1 A(z) so that the supercriticality condition implies that A( C ) 1 and the (dominant) singularity C of C(x) is a pole. This notion of supercriticality is borrowed from Soria [59] who showed it to be determinant in the probabilistic properties of sequences. Literally taken, the Boltzmann sampler C of Section 3 taken with x = C loops forever and generates objects of in nite size, as it produces a number of components equal to a Geom(1) This prevents us from using the ....

Soria-Cousineau, M. Methodes d'analyse pour les constructions combinatoires et les algorithmes. Doctorat es sciences, Universite de Paris{Sud, Orsay, July 1990.

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