Limitations of self-assembly at temperature 1

We prove that if a set X ⊆ Z2 weakly self-assembles at temperature 1 in a deterministic (Winfree) tile assembly system satisfying a natural condition known as pumpability, then X is a finite union of semi-doubly periodic sets. This shows that only the most simple of infinite shapes and patterns can be constructed using pumpable temperature 1 tile assembly systems, and gives evidence for the thesis that temperature 2 or higher is required to carry out general-purpose computation in a tile assembly system. Finally, we show that general-purpose computation is possible at temperature 1 if negative glue strengths are allowed in the tile assembly model.

• Type: Journal
• Year: 2011
• Where: TCS
• Authors: David Doty, Matthew J. Patitz, Scott M. Summers
• Keywords: General-purpose Computation, TCS 2011, Theoretical Computer Science, Tile Assembly, Tile Assembly Systems