Strict Self-Assembly

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.

See also

Weak Self-Assembly