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International Conference on Unconventional Computing and Natural Computation

UCNC 2013: Unconventional Computation and Natural Computation pp 174–185Cite as

Asynchronous Signal Passing for Tile Self-assembly: Fuel Efficient Computation and Efficient Assembly of Shapes

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7956))

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.

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Author information

Authors and Affiliations

  1. Department of Chemistry, New York University, New York, NY, 10003, USA

    Jennifer E. Padilla & Nadrian C. Seeman

  2. Department of Computer Science and Computer Engineering, University of Arkansas, Fayetteville, AR, 72701, USA

    Matthew J. Patitz

  3. Department of Computer Science, University of Texas – Pan American, Edinburg, TX, 78539, USA

    Raul Pena, Robert T. Schweller, Robert Sheline & Xingsi Zhong

  4. Department of Computer Science and Software Engineering, University of Wisconsin – Platteville, Platteville, WI, 53818, USA

    Scott M. Summers

Authors
  1. Jennifer E. Padilla
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  2. Matthew J. Patitz
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  3. Raul Pena
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  4. Robert T. Schweller
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  5. Nadrian C. Seeman
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  6. Robert Sheline
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  7. Scott M. Summers
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  8. Xingsi Zhong
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Editor information

Editors and Affiliations

  1. Dipartimento di Informatica, Sistemistica e Communicazione, Università degli Studi di Milano-Bicocca, Viale Sacra 336/14, 20126, Milan, Italy

    Giancarlo Mauri

  2. Dipartimento di Informatica, Sistemistica e Comunicazione, Università degli Studi di Milano–Bicocca, Viale Sarca 336, 20126, Milano, Italy

    Alberto Dennunzio  & Luca Manzoni  & 

  3. Dipartimento di Informatica, Sistemistica e Comunicazione, Università degli Studi di Milano-Bicocca, Viale Sarca 336/14, 20126, Milano, Italy

    Antonio E. Porreca

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Padilla, J.E. et al. (2013). Asynchronous Signal Passing for Tile Self-assembly: Fuel Efficient Computation and Efficient Assembly of Shapes. In: Mauri, G., Dennunzio, A., Manzoni, L., Porreca, A.E. (eds) Unconventional Computation and Natural Computation. UCNC 2013. Lecture Notes in Computer Science, vol 7956. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39074-6_17

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  • DOI: https://doi.org/10.1007/978-3-642-39074-6_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-39073-9

  • Online ISBN: 978-3-642-39074-6

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