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Complexity of Self-assembled Shapes (Extended Abstract)

Soloveichik, David and Winfree, Erik (2005) Complexity of Self-assembled Shapes (Extended Abstract). In: DNA Computing. Lecture Notes in Computer Science. No.3384. Springer , Berlin, pp. 344-354. ISBN 978-3-540-26174-2. https://resolver.caltech.edu/CaltechAUTHORS:20200221-095747956

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Abstract

The connection between self-assembly and computation suggests that a shape can be considered the output of a self-assembly “program,” a set of tiles that fit together to create a shape. It seems plausible that the size of the smallest self-assembly program that builds a shape and the shape’s descriptional (Kolmogorov) complexity should be related. We show that under the notion of a shape that is independent of scale this is indeed so: in the Tile Assembly Model, the minimal number of distinct tile types necessary to self-assemble an arbitrarily scaled shape can be bounded both above and below in terms of the shape’s Kolmogorov complexity. As part of the proof of the main result, we sketch a general method for converting a program outputting a shape as a list of locations into a set of tile types that self-assembles into a scaled up version of that shape. Our result implies, somewhat counter-intuitively, that self-assembly of a scaled up version of a shape often requires fewer tile types, and suggests that the independence of scale in self-assembly theory plays the same crucial role as the independence of running time in the theory of computability.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://doi.org/10.1007/11493785_30DOIArticle
https://arxiv.org/abs/cs/0412096arXivDiscussion Paper
https://rdcu.be/b3YocPublisherFree ReadCube access
ORCID:
AuthorORCID
Soloveichik, David0000-0002-2585-4120
Winfree, Erik0000-0002-5899-7523
Additional Information:© 2005 Springer-Verlag Berlin Heidelberg. We thank Len Adleman, members of his group, and Paul Rothemund for fruitful discussions and suggestions. We thank Rebecca Schulman and David Zhang for useful and entertaining conversations about descriptional complexity of tile systems. This work was supported by NSF CAREER Grant No. 0093486.
Funders:
Funding AgencyGrant Number
NSFCNS-0093486
Series Name:Lecture Notes in Computer Science
Issue or Number:3384
Record Number:CaltechAUTHORS:20200221-095747956
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200221-095747956
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:101452
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:21 Feb 2020 18:08
Last Modified:05 May 2020 23:03

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