conferência - CNRS Brasil
CÁTEDRA CLAUDE BERNARD
(UNIVERSIDADE FEDERAL DO RIO DE JANEIRO –
COLLÈGE DE FRANCE – ACADEMIA BRASILEIRA DE
CIÊNCIAS – ACADEMIA FRANCESA DE CIÊNCIAS)
Data: quarta-feira, 04 de setembro de 2013.
Local: Salão Nobre do Centro de Tecnologia, Bloco A, 2º andar, CT/UFRJ,
Ilha do Fundão.
Conferencista: Professor Gérard BERRY, Collège de France, Paris.
Título: Circuits and 2-adic numbers
Hensel’s p-adic numbers (1897) are numbers written with an infinity of digits in base p,
but, contrarily to the real numbers, low-order digits first. They play a major role in
several areas of mathematics and in particular in number theory. Contrarily to the real
numbers, they have never had a physical interpretation; therefore, they used to be
considered as pure mathematical objects, not related to any kind of applications. But
their situation is different in informatics, which can be seen as a form of “synthetic
physics”: real numbers are not computable and thus not really meaningful in
informatics, while p-adic numbers have very natural computational interpretations. We
discuss the pioneering work of Jean Vuillemin, who showed that 2-adic numbers unify
logic and arithmetic and directly relate to digital circuits, and in particular to arithmetic
ones. We show that Vuillemin’s 2-adic view gives a new and much simpler view of
combinational and serial arithmetic, makes it possible to design remarkably elegant
circuits (some of them being true jewels), and to clarify the question of time / space
tradeoff and exchange in circuits. No prior knowledge of p-adic arithmetic is required
for the talk.
Consulado Geral da França no Rio de Janeiro
INCT: WEB-SCIENCE (CNPq e FAPERJ)
Programa de Engenharia de Sistemas e Computação, COPPE, UFRJ.
Instituto de Matemática, UFRJ.
Responsáveis na UFRJ:
Nelson Maculan([email protected]) e Luiz Davidovich ([email protected])
tel.: + 55 21 2562-8708