Abstract
In this paper we demonstrate the power of a model of tile self-assembly based on active glues which can dynamically change state. We formulate the Signal-passing Tile Assembly Model (STAM), based on the model of Padilla et al. [24] to be asynchronous, allowing any action of turning a glue on or off, attaching a new tile, or breaking apart an assembly to happen in any order. Within this highly generalized model we provide three new solutions to tile self-assembly problems that have been addressed within the abstract Tile Assembly Model and its variants, showing that signal passing tiles allow for substantial improvement across multiple complexity metrics. Our first result utilizes a recursive assembly process to achieve tile-type efficient assembly of linear structures, using provably fewer tile types than what is possible in standard tile assembly models. Our second system of signal-passing tiles simulates any Turing machine with high fuel efficiency by using only a constant number of tiles per computation step. Our third system assembles the discrete Sierpinski triangle, demonstrating that this pattern can be strictly self-assembled within the STAM. This result is of particular interest in that it is known that this pattern cannot self-assemble within a number of well studied tile self-assembly models. Notably, all of our constructions are at temperature 1, further demonstrating that signal-passing confers the power to bypass many restrictions found in standard tile assembly models.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 459-488 |
| Number of pages | 30 |
| Journal | International Journal of Foundations of Computer Science |
| Volume | 25 |
| Issue number | 4 |
| DOIs | |
| State | Published - 2014 |
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Keywords
- asynchronous behavior
- Self-assembly
- Tile Assembly Model
- universal computation
ASJC Scopus subject areas
- Computer Science (miscellaneous)
Cite this
Asynchronous signal passing for tile self-assembly : Fuel efficient computation and efficient assembly of shapes. / Padilla, Jennifer E.; Patitz, Matthew J.; Schweller, Robert T.; Seeman, Nadrian; Summers, Scott M.; Zhong, Xingsi.
In: International Journal of Foundations of Computer Science, Vol. 25, No. 4, 2014, p. 459-488.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Asynchronous signal passing for tile self-assembly
T2 - Fuel efficient computation and efficient assembly of shapes
AU - Padilla, Jennifer E.
AU - Patitz, Matthew J.
AU - Schweller, Robert T.
AU - Seeman, Nadrian
AU - Summers, Scott M.
AU - Zhong, Xingsi
PY - 2014
Y1 - 2014
N2 - In this paper we demonstrate the power of a model of tile self-assembly based on active glues which can dynamically change state. We formulate the Signal-passing Tile Assembly Model (STAM), based on the model of Padilla et al. [24] to be asynchronous, allowing any action of turning a glue on or off, attaching a new tile, or breaking apart an assembly to happen in any order. Within this highly generalized model we provide three new solutions to tile self-assembly problems that have been addressed within the abstract Tile Assembly Model and its variants, showing that signal passing tiles allow for substantial improvement across multiple complexity metrics. Our first result utilizes a recursive assembly process to achieve tile-type efficient assembly of linear structures, using provably fewer tile types than what is possible in standard tile assembly models. Our second system of signal-passing tiles simulates any Turing machine with high fuel efficiency by using only a constant number of tiles per computation step. Our third system assembles the discrete Sierpinski triangle, demonstrating that this pattern can be strictly self-assembled within the STAM. This result is of particular interest in that it is known that this pattern cannot self-assemble within a number of well studied tile self-assembly models. Notably, all of our constructions are at temperature 1, further demonstrating that signal-passing confers the power to bypass many restrictions found in standard tile assembly models.
AB - In this paper we demonstrate the power of a model of tile self-assembly based on active glues which can dynamically change state. We formulate the Signal-passing Tile Assembly Model (STAM), based on the model of Padilla et al. [24] to be asynchronous, allowing any action of turning a glue on or off, attaching a new tile, or breaking apart an assembly to happen in any order. Within this highly generalized model we provide three new solutions to tile self-assembly problems that have been addressed within the abstract Tile Assembly Model and its variants, showing that signal passing tiles allow for substantial improvement across multiple complexity metrics. Our first result utilizes a recursive assembly process to achieve tile-type efficient assembly of linear structures, using provably fewer tile types than what is possible in standard tile assembly models. Our second system of signal-passing tiles simulates any Turing machine with high fuel efficiency by using only a constant number of tiles per computation step. Our third system assembles the discrete Sierpinski triangle, demonstrating that this pattern can be strictly self-assembled within the STAM. This result is of particular interest in that it is known that this pattern cannot self-assemble within a number of well studied tile self-assembly models. Notably, all of our constructions are at temperature 1, further demonstrating that signal-passing confers the power to bypass many restrictions found in standard tile assembly models.
KW - asynchronous behavior
KW - Self-assembly
KW - Tile Assembly Model
KW - universal computation
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UR - http://www.scopus.com/inward/citedby.url?scp=84905994021&partnerID=8YFLogxK
U2 - 10.1142/S0129054114400061
DO - 10.1142/S0129054114400061
M3 - Article
AN - SCOPUS:84905994021
VL - 25
SP - 459
EP - 488
JO - International Journal of Foundations of Computer Science
JF - International Journal of Foundations of Computer Science
SN - 0129-0541
IS - 4
ER -