Euclideans Dynamics

Brigitte Vallée (1)

1 Equipe AMACC - Laboratoire GREYC - UMR6072

We study a general class of Euclidean algorithms which compute the greatest common divisor [gcd], and we perform probabilistic analyses of their main parameters. We view an algorithm as a dynamical system restricted to rational inputs, and combine tools imported from dynamics, such as transfer operators, with various tools of analytic combinatorics: generating functions, Dirichlet series, Tauberian theorems, Perron's formula, quasi-powers theorems. Such dynamical analyses can be used to perform the average-case analysis of algorithms, but also (dynamical) analysis in distribution.

Domaines: Algorithme et structure de données [cs.DS]

Brigitte Vallée. Euclideans Dynamics. Discrete and Continuous Dynamical Systems - Series S, 2006, pp.281-352. ⟨hal-00204770⟩