Universal Shape Replicators via Self-Assembly with Attractive and Repulsive Forces
Name
Universal shape replicators via self-assembly with attractive and repulsive forces.pdf
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1.48 MB
Format
Adobe PDF
Checksum (MD5)
7058e3c45d9d8dd18ad71ef086899bb5
Author(s)
Chalk, Cameron
Martinez, Eric
Schweller, Robert
Vega, Luis
Wylie, Tim
Demaine, Erik D
Demaine, Martin L
Date Issued
January 2017
Journal
Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms
Publisher
Society for Industrial and Applied Mathematics
Citation
Chalk, Cameron, et al. "Universal Shape Replicators via Self-Assembly with Attractive and Repulsive Forces." Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms, 16-19 January, 2017, Barcelona, Spain, Society for Industrial and Applied Mathematics, 2017, pp. 225–38.
Version
Author's final manuscript
Abstract
We show how to design a universal shape replicator in a self- assembly system with both attractive and repulsive forces. More precisely, we show that there is a universal set of constant-size objects that, when added to any unknown holefree polyomino shape, produces an unbounded number of copies of that shape (plus constant-size garbage objects). The constant-size objects can be easily constructed from a constant number of individual tile types using a constant number of preprocessing self-assembly steps. Our construction uses the well-studied 2-Handed Assembly Model (2HAM) of tile self-assembly, in the simple model where glues interact only with identical glues, allowing glue strengths that are either positive (attractive) or negative (repulsive), and constant temperature (required glue strength for parts to hold together). We also require that the given shape has specified glue types on its surface, and that the feature size (smallest distance between nonincident edges) is bounded below by a constant. Shape replication necessarily requires a self-assembly model where parts can both attach and detach, and this construction is the first to do so using the natural model of negative/repulsive glues (also studied before for other problems such as fuel-efficient computation); previous replication constructions require more powerful global operations such as an “enzyme” that destroys a subset of the tile types.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1137/1.9781611974782.15
