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Mardi 26 Mai
Heure: |
14:00 - 17:00 |
Lieu: |
Salle B107, bâtiment B, Université de Villetaneuse |
Résumé: |
Efficient Algebraic Diagonals and Walks |
Description: |
Louis Dumont The diagonal of a multivariate power series F is the univariate power series Diag F generated by the diagonal terms of F. Diagonals form an important class of power series; they occur frequently in number theory, theoretical physics and enumerative combinatorics. Westudy algorithmic questions related to diagonals in the case where F is the Taylor expansion of a bivariate rational function. It is classical that in this case Diag F is an algebraic function. We propose an algorithm that computes an annihilating polynomial forDiag F. Generically, it is its minimal polynomial and is obtained in time quasi-linear in its size. We show that this minimal polynomial has an exponential size with respect to the degree of the input rational function. Throughout the talk, we use a common problemof counting certain lattice walks to illustrate the capacities and limits of our tools. |
Mercredi 27 Mai
Heure: |
14:00 - 16:00 |
Lieu: |
Salle B107, bâtiment B, Université de Villetaneuse |
Résumé: |
Logics via algebras and substitutions |
Description: |
Antonino Salibra In this talk we present a translation of formulas and models of classical and non-classical logics into factor algebras. The correspondence: Propositional variables --- operator of decompositions Logical operations --- substitutions Formulas --- algebraic terms Models --- factor algebras, provides a uniform calculus of provability for all the logics which admit the translation. Many examples will be discussed: classical logic, intuitionistic logic, linear logic, many-valued logics. |
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