GENERATING SERIES : A COMBINATORIAL COMPUTATION

Farida Benmakrouha (1) , Hespel Christiane (1)

1 IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires

The purpose of this paper is to apply combinatorial techniques for computing coefficients of rational formal series (Gk) in two noncommuting variables and their differences at orders k and k-1. This in turn may help one to study the reliability and the quality of a model for non-linear black-box identification. We investigate the quality of the model throughout the criteria of a measure of convergence. We provide, by a symbolic computation, a valuation relating to the convergence of the family (Bk). This computation is a sum of differ- ential monomials in the input functions and behavior system. We identify each differential monomial with its colored multiplicity and analyse our computation in the light of the free differential calcu- lus. We propose also a combinatorial interpretation of coefficients of (Gk). These coefficients are powers of an operator Θ which is in the monoid generated by two linear differential operators ∆ and Γ. More than a symbolic validation, these computing tools are param- eterized by the input and the system's behavior.

Mots clés: nonlinear systems; combinatorics; generating series; symbolic computation; model validation.; model validation

Domaines: Informatique et langage [cs.CL]; Calcul formel [cs.SC]

Farida Benmakrouha, Hespel Christiane. GENERATING SERIES : A COMBINATORIAL COMPUTATION. Journal of Nonlinear Systems and Applications, 2010, 1 (1-2), p. 72-79. ⟨hal-00566581⟩