Context-free Coalgebras

In this article, we provide a coalgebraic account of parts of the mathematical theory underlying context-free languages. We characterize context-free languages, and power series and streams generalizing or corresponding to the context-free languages, by means of systems of behavioural differential equations; and prove a number of results, some of which are new, and some of which are new proofs of existing theorems, using the techniques of bisimulation and bisimulation up to linear combinations. Furthermore, we establish a link between automatic sequences and these systems of equations, allowing us to, given an automaton generating an automatic sequence, easily construct a system of behavioural differential equations yielding this sequence as a context-free stream

Nonnegative Rank Measures and Monotone Algebraic Branching Programs

Inspired by Nisan\u27s characterization of noncommutative complexity (Nisan 1991), we study different notions of nonnegative rank, associated complexity measures and their link with monotone computations. In particular we answer negatively an open question of Nisan asking whether nonnegative rank characterizes monotone noncommutative complexity for algebraic branching programs. We also prove a rather tight lower bound for the computation of elementary symmetric polynomials by algebraic branching programs in the monotone setting or, equivalently, in the homogeneous syntactically multilinear setting

Au Sujet des Approches Symboliques des Équations Intégro-Différentielles

International audienceRecent progress in computer algebra has opened new opportunities for the parameter estimation problem in nonlinear control theory, by means of integro-differential input-output equations. This paper recalls the origin of integro-differential equations. It presents new opportunities in nonlinear control theory. Finally, it reviews related recent theoretical approaches on integro-differential algebras, illustrating what an integro-differential elimination method might be and what benefits the parameter estimation problem would gain from it.Un résultat récent en calcul formel a ouvert de nouvelles opportunités pour l'estimation de paramètres en théorie du contrôle non linéaire, via des équations entrée-sortie intégro-différentielles. Ce chapitre rappelle les origines des équations intégro-différentielles. Il présente de nouvelles opportunités en théorie du contrôle non linéaire. Finalement, il passe en revue des approches théoriques récentes sur les algèbres intégro-différentielles, illustrant ce qu'une méthode d'élimination intégro-différentielle pourrait être et les bénéfices que le problème de l'estimation de paramètres pourrait en tirer

Learning weighted automata over principal ideal domains

In this paper, we study active learning algorithms for weighted automata over a semiring. We show that a variant of Angluin’s seminal L⋆ algorithm works when the semiring is a principal ideal domain, but not for general semirings such as the natural numbers