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Kolmogorov complexity --- Kolmogorov complexity.

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This book has been written in the hope that readers will be able to absorb the key ideas behind algorithmic information theory so that they are in a better position to access the mathematical developments and to apply the ideas to their own areas of interest.

Information theory. --- Kolmogorov complexity.

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Kolmogorov complexity. --- Kolmogorov complexity --- Kolmogorov, Complexité de --- 681.3*F --- Complexity, Kolmogorov --- Kolmogorov-Chaitin complexity --- Machine theory --- Theory of computation --- 681.3*F Theory of computation --- Kolmogorov, Complexité de --- #TELE:SISTA --- Electronic data processing --- Computer science --- Number theory

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Algorithmic information theory (AIT), or Kolmogorov complexity as it is known to mathematicians, can provide a useful tool for scientists to look at natural systems, however some critical conceptual issues need to be understood and the advances already made collated and put in a form accessible to scientists. This book has been written in the hope that readers will be able to absorb the key ideas behind AIT so that they are in a better position to access the mathematical developments and to apply the ideas to their own areas of interest. The theoretical underpinning of AIT is outlined in the earlier chapters, while later chapters focus on the applications, drawing attention to the thermodynamic commonality between ordered physical systems such as the alignment of magnetic spins, the maintenance of a laser distant from equilibrium, and ordered living systems such as bacterial systems, an ecology, and an economy.

Kolmogorov complexity. --- Information theory. --- COMPUTERS / Information Theory.

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On entend souvent dire aujourd'hui que la complexité est devenue un problème fondamental de la science contemporaine, car toutes les disciplines y sont confrontées, et cela sous une multitude de formes. Avant de pouvoir confirmer une telle affirmation, une série de questions se posent : Qu'est-ce que la complexité ? Y a-t-il un concept précis derrière le mot ? Que nous disent les mathématiques sur de possibles définitions formelles ? Quelles sont les conséquences et les applications du travail de définition théorique ? Ces questions, qui trouvent leur réponse dans ce livre, intéresseront à la fois les mathématiciens, les statisticiens, les biologistes et tous les étudiants des grandes écoles d'ingénieur, mais aussi tous ceux qui veulent comprendre la philosophie des sciences contemporaines dont l'un des buts est de saisir la nature profonde du hasard et de la complexité.

Kolmogorov complexity --- Computational complexity --- Logic, Symbolic and mathematical --- Mathematical analysis.