La machine \alpha: mod\`ele g\'en\'erique pour les algorithmes naturels

TL;DR

This paper introduces the machine-alpha, a universal model of algorithms that extends Turing's concept to better encompass natural, massively parallel, self-adaptive, and reproductive algorithms, including communication and randomness.

Contribution

It proposes a new theoretical model, machine-alpha, that generalizes existing models to include features like communication, evolution, and randomness found in natural algorithms.

Findings

Machine-alpha unifies existing algorithm models.

It accounts for communication and evolutionary rules.

It provides a framework for natural algorithms.

Abstract

So far, following the works of A.M. Turing, the algorithms were considered as the mathematical abstraction from which we could write programs for computers whose principle was based on the theoretical concept of Turing machine. We start here from the observation that natural algorithms or rather algorithms of the nature which are massively parallel, autoadaptative and reproductible, and for which we do not know how they really work, nor why, are not easily specified by the current theoretical model of Universal Turing machine, or Universal Computer. In particular the aspects of communications, evolutionary rules (rulers), random (unpredictable) events, just like the genetic code, are taken into account only by subtleties which oblige to break the theory. We shall propose one \textit{universal model} of algorithm called machine-alpha which contains and generalizes the existing models. --- Jusqu'ici, suite aux travaux de A.M.Turing [Turing, 1936], les algorithmes ont \'et\'e vus comme l'abstraction \`a partir de laquelle on pouvait \'ecrire des programmes pour des ordinateurs dont le principe \'etait lui-m\^eme issu du concept th\'eorique de machine de Turing. Nous partons ici du constat que les algorithmes naturels ou plut\^ot les algorithmes de la nature, massivement parall\`eles, autoadaptatifs et auto reproductibles, dont on ne sait pas comment ils fonctionnent r\'eellement, ni pourquoi, ne sont pas ais\'ement sp\'ecifi\'es par le mod\`ele th\'eorique actuel de Machine de Turing Universelle, ou de Calculateur Universel ; en particulier les aspects de communications, de r\`egles \'evolutives, d' \'ev\'enements al\'eatoires, \`a l'image du code g\'en\'etique, ne sont pris en compte que par ajout d'artifices \`a la th\'eorie. Nous nous proposons ici de montrer comment aborder ces probl\`emes en repensant le mod\`ele th\'eorique. Nous proposerons un mod\`ele d'algorithme, appel\'e ici machine-\alpha qui contient et g\'en\'eralise les mod\`eles existants.