Abstract
We introduce a new property of tile self-assembly systems that we call size-separability. A system is size-separable if every terminal assembly is a constant factor larger than any intermediate assembly. Size-separability is motivated by the practical problem of filtering completed assemblies from a variety of incomplete “garbage” assemblies using gel electrophoresis or other mass-based filtering techniques. Here we prove that any system without cooperative bonding assembling a unique mismatch-free terminal assembly can be used to construct a size-separable system uniquely assembling the same shape. The proof achieves optimal scale factor, temperature, and tile types (within a factor of 2) for the size-separable system.
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Notes
Otherwise \(\mathcal {S}\) has a second terminal assembly containing a tile type not found in A.
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The author thanks the anonymous UCNC and Natural Computation reviewers for their comments that improved the presentation and correctness of the paper.
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An extended abstract of this work was previously published in Unconventional Computation and Natural Computation, LNCS, vol. 8553, pp. 367–378, Springer Berlin Heidelberg (2014).
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Winslow, A. Size-separable tile self-assembly: a tight bound for temperature-1 mismatch-free systems. Nat Comput 15, 143–151 (2016). https://doi.org/10.1007/s11047-015-9516-3
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DOI: https://doi.org/10.1007/s11047-015-9516-3