This book presents a unified approach to a rich and rapidly evolving research domain at the interface between statistical physics, theoretical computer science/discrete mathematics, and coding/information theory. It is accessible to graduate students and researchers without a specific training in any of these fields. The selected topics include spin glasses, error correcting codes, satisfiability, and are central to each field. The approach focuses on large random instances and adopts a common probabilistic formulation in terms of graphical models. It presents message passing algorithms like belief propagation and survey propagation, and their use in decoding and constraint satisfaction solving. It also explains analysis techniques like density evolution and the cavity method, and uses them to study phase transitions.

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Professor Marc Mezard
CNRS Research Director at Universit� de Paris Sud and Professor at Ecole Polytechnique, France

Marc Mezard received his PhD in 1984. He was hired in CNRS in 1981 and became research director in 1990 at Ecole Normale Sup�rieure. He joined the Universit� Paris Sud in 2001. He spent extensive periods in Rome University, in the KITP (Santa Barbara) and in MSRI (Berkeley). Author of about 150 publications, he has been
awarded the silver medal of CNRS in 1990 and the Ampere price of the French academy of science in 1996.

Dr Andrea Montanari
Assistant Professor, Stanford University and CNRS France

Andrea Montanari received a Laurea degree in Physics in 1997, and a Ph. D. in Theoretical Physics in 2001 (both from Scuola Normale Superiore in Pisa, Italy). He has been post-doctoral fellow at Laboratoire de Physique Th�orique de l'Ecole Normale Sup�rieure (LPTENS), Paris, France, and the Mathematical Sciences Research Institute, Berkeley, USA. Since 2002 he is Charg� de Recherche (a permanent research position with Centre National de la Recherche Scientifique, CNRS) at LPTENS.
In September 2006 he joined Stanford University as Assistant Professor in the Departments of Electrical Engineering and Statistics.
In 2006 he was awarded the CNRS bronze medal for theoretical physics.

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