Phase transitions and complexity in computer science: an overview of the statistical physics approach to the random satisfiability problem

Phase transitions, ubiquitous in condensed matter physics, are encountered in computer science too. The existence of critical phenomena has deep consequences on computational complexity, that is the resolution times of various optimization or decision problems. Concepts and methods borrowed from the statistical physics of disordered and out-of-equilibrium systems shed new light on the dynamical operation of solving algorithms.