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2011

Limitations of self-assembly at temperature 1

8 years 1 months ago
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.
David Doty, Matthew J. Patitz, Scott M. Summers
Added 15 May 2011
Updated 15 May 2011
Type Journal
Year 2011
Where TCS
Authors David Doty, Matthew J. Patitz, Scott M. Summers
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