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Complexite aleatoire et complexite

by Jean-Paul Delahaye (writer)

may 2009

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Summary

It is often said these days that complexity has become a fundamental problem in modern science, as it concerns each and every discipline, in a multitude of shapes and forms. Before such a claim can be confirmed, there are several questions to be answered: What is complexity? Is there a precise concept behind the word? What can mathematics tell us about possible formal definitions? What are the consequences and applications of work to find a theoretical definition?
These questions, which are answered in the book, will be of interest to mathematicians, statisticians, biologists and engineering students at French grandes écoles, but also anyone looking to understand the philosophy of modern science, one of the aims of which is to grasp the profound nature of chance and complexity.

Introduction

Deux complexite´s ?

La complexite´ ale´atoire
Pourquoi se ramener a` une suite de 0 et de 1 ?
La de´finition de´pend-elle du langage de programmation choisi ?

Des exemples pour e´clairer la de´finition
Une suite re´pe´titive e´le´mentaire
Un milliard de chiffres du de´veloppement en base 2 du nombre p
Une suite de chiffres au hasard
Un exemple mixte

Le calcul et l'e´valuation de K(s)

Complexite´ relative et distance informationnelle

La complexite´ de Kolmogorov, mesure de la complexite´ ale´atoire

Premie`re tentative de de´finition du contenu en calcul

Deuxie`me tentative de de´finition du contenu en calcul

Troisie`me tentative de de´finition du contenu en calcul

Arguments favorables a` l'identification propose´e par Bennett

Autres ide´es et propositions

Conclusion

Bibliographie

Discussion

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Complexite aleatoire et complexite

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