License: Creative Commons Attribution-NoDerivs 3.0 Unported license (CC BY-ND 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2013.172
URN: urn:nbn:de:0030-drops-39321
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2013/3932/
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Cannon, Sarah ; Demaine, Erik D. ; Demaine, Martin L. ; Eisenstat, Sarah ; Patitz, Matthew J. ; Schweller, Robert T. ; Summers, Scott M ; Winslow, Andrew

Two Hands Are Better Than One (up to constant factors): Self-Assembly In The 2HAM vs. aTAM

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Abstract

We study the difference between the standard seeded model (aTAM) of tile self-assembly, and the "seedless" two-handed model of tile self-assembly (2HAM). Most of our results suggest that the two-handed model is more powerful. In particular, we show how to simulate any seeded system with a two-handed system that is essentially just a constant factor larger. We exhibit finite shapes with a busy-beaver separation in the number of distinct tiles required by seeded versus two-handed, and exhibit an infinite shape that can be constructed two-handed but not seeded. Finally, we show that verifying whether a given system uniquely assembles a desired supertile is co-NP-complete in the two-handed model, while it was known to be polynomially solvable in the seeded model.

BibTeX - Entry

@InProceedings{cannon_et_al:LIPIcs:2013:3932,
  author =	{Sarah Cannon and Erik D. Demaine and Martin L. Demaine and Sarah Eisenstat and Matthew J. Patitz and Robert T. Schweller and Scott M Summers and Andrew Winslow},
  title =	{{Two Hands Are Better Than One (up to constant factors): Self-Assembly In The 2HAM vs. aTAM}},
  booktitle =	{30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
  pages =	{172--184},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-50-7},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{20},
  editor =	{Natacha Portier and Thomas Wilke},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2013/3932},
  URN =		{urn:nbn:de:0030-drops-39321},
  doi =		{10.4230/LIPIcs.STACS.2013.172},
  annote =	{Keywords: abstract tile assembly model, hierarchical tile assembly model, two-handed tile assembly model, algorithmic self-assembly, DNA computing, biocomputing}
}

Keywords: abstract tile assembly model, hierarchical tile assembly model, two-handed tile assembly model, algorithmic self-assembly, DNA computing, biocomputing
Collection: 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)
Issue Date: 2013
Date of publication: 26.02.2013

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