A Minimal Requirement for Self-assembly of Lines in Polylogarithmic Time
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. 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.
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.
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