Tile Assembly System (TAS)

Overview

Informally, a tile assembly system can be thought of as an instance of a tile assembly model. Unless otherwise denoted, a tile assembly system refers to a tile assembly system of the abstract tile assembly model.

Abstract Tile Assembly Model Tile Assembly System (aTAM TAS)

A tile assembly system (TAS) of the abstract tile assembly model is an ordered triple \(\mathcal{T} = (T, \sigma, \tau)\), where \(T\) is a finite set of tile types, \(\sigma\) is a seed assembly with finite domain, and \(\tau \in \mathbb{N}\).

Abstract Tile Assembly Model Generalized Tile Assembly System (aTAM GTAS)

A generalized tile assembly system (GTAS) of the abstract tile assembly model is an ordered triple \(\mathcal{T} = (T, \sigma, \tau)\), where \(T\) is a not necessarily finite set of tile types, \(\sigma\) is a seed assembly with finite domain, and \(\tau \in \mathbb{N}\). Note the only difference between the aTAM GTAS and the aTAM TAS is that the aTAM TAS requires the tile set to be finite.