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The present paper exposes algorithmic results providing a vision about sleep functions which complements biological theory and experiments. Derived from the algorithmic theory of information, the theory of adaptation aims at quantifying how an inherited or acquired piece of knowledge helps individuals to survive. It gives a scale of complexity for survival problems and proves that some of them can only be solved by a dynamical management of memory associating continuous learning and forgetting methods. In this paper we explain how a virtual robot “Picota” has been designed to simulate the behavior of a living hen. In order to survive in its synthetical environnement, our robot must recognize good seeds from bad ones, and should take rest during night periods. Within this frame, and facing the rapid evolution of to-be-recognized forms, the best way to equilibrate the energetic needs of the robot and ensure survival is to use the nightly rest to reorganize the pieces of data acquired during the daily learning, and to trash the less useful ones. Thanks to this time sharing, the same circuits can be used for both daily learning and nightly forgetting and thus costs are lower ; however, this also forces the system to “paralyse” the virtual robot, and therefore the night algorithm is reminiscent of paradoxical (REM) sleep. The algorithm of the robot takes advantage of the alternation between wakefulness or activity and the rest period. This diagram quite accurately recalls the REM period. In the future, the convergence between the neurophysiology of sleep and the theory of complexity may give us a new line of research in order to elucidate sleep functions. [Copyright &y& Elsevier]