A minimal requirement for self-assembly of lines in polylogarithmic time

Abstract

Self-assembly is the process in which small and simple components assemble into large and complex structures without explicit external control. The nubot model generalizes previous self-assembly models (e.g. the abstract Tile Assembly Model (aTAM)) to include active components which can actively move and undergo state changes. One main difference between the nubot model and previous self-assembly models is its ability to perform exponential growth with respect to time. In the paper, we study the problem of finding a minimal set of features in the nubot model which allows exponential growth to happen. We only focus on nubot systems which assemble a long line of nubots with a small number of supplementary layers. We prove that exponential growth is not possible with the limit of one supplementary layer and one state-change per nubot. On the other hand, if two supplementary layers are allowed, or the disappearance rule can be performed without a state change, then we can construct nubot systems which grow exponentially.