In this paper, we consider non-deterministic tree transducers in the letter to letter case, that is to say tree transducers for which trees which appear in the rules are reduced to one letter in the right-hand side as in the left one. We establish the decidability of equivalence for linear and non-deleting top-down transducers. These results are valid in the bottom-up case. R'esum'e Nous consid'erons des transducteurs non d'eterministes d'arbres dans le cas lettre `a lettre. Nous 'etablissons la d'ecidabilit'e de l"equivalence pour les transducteurs descendants lin'eaires et complets. Ces r'esultats s"etendent au cas des transducteurs ascendants. 2 1 Introduction Tree transducers, which are a generalization of rational transformations in the word case (see [1], [3] for a synthesis), were introduced by W.C. Rounds [15] and J.W. Thatcher [17]. They have been widely studied. The authors have chosen either the algebraic point of view ([2], [9], [4]), or the machine point of view ([7], ...

Abstract. This paper is devoted to the presentation of the key concepts on which a mathematical theory of complex (industrial) systems can be based. We especially show how this formal framework can capture the realness of modern information technologies. We also present some new modelling problems that are naturally emerging in the specific context of complex software systems.

In this paper, we present first a brief survey of some techniques in regular grammar inference. The core of the discussion is then to try to classify these different methods within a unique framework. A first step in that direction [10] has introduced a general methodology based on letter-to-letter morphisms. We pursue that work and propose successively paradigms based on rewriting morphisms, substitutions, and transductions.