Asynchronous signal passing for tile self-assembly: Fuel efficient computation and efficient assembly of shapes

Jennifer E. Padilla, Matthew J. Patitz, Raul Pena, Robert T. Schweller, Nadrian Seeman, Robert Sheline, Scott M. Summers, Xingsi Zhong

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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.[1] 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 languageEnglish (US)
Title of host publicationUnconventional Computation and Natural Computation - 12th International Conference, UCNC 2013, Proceedings
Pages174-185
Number of pages12
Volume7956 LNCS
DOIs
StatePublished - 2013
Event12th International Conference on Unconventional Computation and Natural Computation, UCNC 2013 - Milan, Italy
Duration: Jul 1 2013Jul 5 2013

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7956 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other12th International Conference on Unconventional Computation and Natural Computation, UCNC 2013
CountryItaly
CityMilan
Period7/1/137/5/13

Fingerprint

Self-assembly
Tile
Self assembly
Glues
Model
Turing machines
Turing Machine
Triangle

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Padilla, J. E., Patitz, M. J., Pena, R., Schweller, R. T., Seeman, N., Sheline, R., ... Zhong, X. (2013). Asynchronous signal passing for tile self-assembly: Fuel efficient computation and efficient assembly of shapes. In Unconventional Computation and Natural Computation - 12th International Conference, UCNC 2013, Proceedings (Vol. 7956 LNCS, pp. 174-185). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7956 LNCS). https://doi.org/10.1007/978-3-642-39074-6-17

Asynchronous signal passing for tile self-assembly : Fuel efficient computation and efficient assembly of shapes. / Padilla, Jennifer E.; Patitz, Matthew J.; Pena, Raul; Schweller, Robert T.; Seeman, Nadrian; Sheline, Robert; Summers, Scott M.; Zhong, Xingsi.

Unconventional Computation and Natural Computation - 12th International Conference, UCNC 2013, Proceedings. Vol. 7956 LNCS 2013. p. 174-185 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7956 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Padilla, JE, Patitz, MJ, Pena, R, Schweller, RT, Seeman, N, Sheline, R, Summers, SM & Zhong, X 2013, Asynchronous signal passing for tile self-assembly: Fuel efficient computation and efficient assembly of shapes. in Unconventional Computation and Natural Computation - 12th International Conference, UCNC 2013, Proceedings. vol. 7956 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 7956 LNCS, pp. 174-185, 12th International Conference on Unconventional Computation and Natural Computation, UCNC 2013, Milan, Italy, 7/1/13. https://doi.org/10.1007/978-3-642-39074-6-17
Padilla JE, Patitz MJ, Pena R, Schweller RT, Seeman N, Sheline R et al. Asynchronous signal passing for tile self-assembly: Fuel efficient computation and efficient assembly of shapes. In Unconventional Computation and Natural Computation - 12th International Conference, UCNC 2013, Proceedings. Vol. 7956 LNCS. 2013. p. 174-185. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-39074-6-17
Padilla, Jennifer E. ; Patitz, Matthew J. ; Pena, Raul ; Schweller, Robert T. ; Seeman, Nadrian ; Sheline, Robert ; Summers, Scott M. ; Zhong, Xingsi. / Asynchronous signal passing for tile self-assembly : Fuel efficient computation and efficient assembly of shapes. Unconventional Computation and Natural Computation - 12th International Conference, UCNC 2013, Proceedings. Vol. 7956 LNCS 2013. pp. 174-185 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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