Abstract
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.
This research was supported in part by National Science Foundation grants 0652569 and 0728806.
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Doty, D., Patitz, M.J., Summers, S.M. (2009). Limitations of Self-assembly at Temperature One. In: Deaton, R., Suyama, A. (eds) DNA Computing and Molecular Programming. DNA 2009. Lecture Notes in Computer Science, vol 5877. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10604-0_4
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DOI: https://doi.org/10.1007/978-3-642-10604-0_4
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