We introduce a model of self-assembly P systems as devices that use some of the features of population P systems to progressively grow a graph structure by forming new bonds between the existing cells and some new cells which are brought into the system step by step. The new cells are then able to self-assemble locally either at the level of cells or at the level of neighbourhoods of cells by using bond-making rules according to a specific self-assembly model. We describe two self-assembly models, called respectively parallel single-point self-assembly and parallel multi-point self-assembly. Then, we precisely state the problem of programmable self-assembly for P systems as the problem of uniquely generating a given graph by means of self-assembly P systems. In this respect, we show how to define a self-assembly P systems that uniquely generates a complete binary tree by using a "minimal" set of resources.
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