Strict Self-Assembly
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Essentially, strict self-assembly means that tiles are only placed in positions defined by the shape. Note that if \(X \in \mathbb{Z}^2\) strictly self-assembles, then \(X\) weakly self-assembles. (Just let the subset of the tile set equal the tile set.)
Definition
A set \(X\) strictly self-assembles if there is a TAS \(\mathcal{T}\) for which every assembly \(\alpha \in \mathcal{A}_{\Box}[\mathcal{T}]\) satisfies \(\dom \alpha = X\). The set \(\mathcal{A}_{\Box}[\mathcal{T}]\) is the set of all terminal assemblies.
