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Erschienen in:
2009 | OriginalPaper | Buchkapitel
Limitations of Self-assembly at Temperature One
verfasst von : David Doty, Matthew J. Patitz, Scott M. Summers
Erschienen in: DNA Computing and Molecular Programming
Verlag: Springer Berlin Heidelberg
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We prove that if a set
X
⊆ ℤ
2
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.