Turing Universality of Step-Wise and Stage Assembly at Temperature 1

In this paper, we investigate the computational power of two variants of Winfree’s abstract Tile Assembly Model [14] at temperature 1: the Stage Tile Assembly Model and the Step-wise Tile Assembly Model. In the Stage Tile Assembly Model, the intermediate assemblies are assembled in several “bins” and they can be mixed in prescribed order and attach together to form more complex structures. The Step-wise Tile Assembly Model is a simplified model of stage assembly in which only one bin is used and assembly happens by attaching tiles one by one to the growing structure.

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