Two Hands Are Better Than One (up to constant factors): Self-Assembly In The 2HAM vs. aTAM
Author(s)Demaine, Erik D.; Demaine, Martin L.; Eisenstat, Sarah Charmian; Cannon, Sarah; Patitz, Matthew J.; Schweller, Robert T.; Summers, Scott M.; Winslow, Andrew; ... Show more Show less
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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.
DepartmentMassachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory; Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Proceedings of the International Symposium on Theoretical Aspects of Computer Science, STACS 2013
Schloss Dagstuhl Publishing
Cannon, Sarah, Erik D. Demaine, Martin L. Demaine, Sarah Eisenstat, Matthew J. Patitz, Scott M. Summers, and Andrew Winslow. "Two Hands Are Better Than One (up to constant factors): Self-Assembly In The 2HAM vs. aTAM." 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013), Feb.27-Mar. 2nd, 2013, Kiel, Germany.
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