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Simulation of Programmable Matter Systems Using Active Tile-Based Self-Assembly

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DNA Computing and Molecular Programming (DNA 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11648))

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Abstract

Self-assembly refers to the process by which small, simple components mix and combine to form complex structures using only local interactions. Designed as a hybrid between tile assembly models and cellular automata, the Tile Automata (TA) model was recently introduced as a platform to help study connections between various models of self-assembly. However, in this paper we present a result in which we use TA to simulate arbitrary systems within the amoebot model, a theoretical model of programmable matter in which the individual components are relatively simple state machines that are able to sense the states of their neighbors and to move via series of expansions and contractions.

We show that for every amoebot system, there is a TA system capable of simulating the local information transmission built into amoebot particles, and that the TA “macrotiles” used to simulate its particles are capable of simulating movement (via attachment and detachment operations) while maintaining the necessary properties of amoebot particle systems. The TA systems are able to utilize only the local interactions of state changes and binding and unbinding along tile edges, but are able to fully simulate the dynamics of these programmable matter systems.

Daymude and Richa are funded in part by the National Science Foundation under awards CCF-1422603, CCF-1637393, and CCF-1733680. Alumbaugh and Patitz are funded in part by National Science Foundation Grants CCF-1422152 and CAREER-1553166.

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Notes

  1. 1.

    Note that there may be ambiguity in choosing a port facing local direction 0; e.g., in Fig. 3c, both port 0 and port 8 face local direction 0. In this case, the port facing local direction 0 and “away” from the particle is labeled 0.

  2. 2.

    Note that this forced scheduling is simply a result of our formalism and does not alter or subvert the underlying asynchrony assumed by the amoebot model.

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Acknowledgements

The authors would like to thank Schloss Dagstuhl – Leibniz Center for Informatics and the organizers and participants of Dagstuhl Seminar 18331 “Algorithmic Foundations of Programmable Matter” [3]. The initial brainstorming and work for this paper began during that workshop and was inspired by many interesting discussions with the participants.

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Authors and Affiliations

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

    John Calvin Alumbaugh & Matthew J. Patitz

  2. Computer Science, CIDSE, Arizona State University, Tempe, AZ, USA

    Joshua J. Daymude & Andréa W. Richa

  3. MIT Computer Science and Artificial Intelligence Laboratory, Cambridge, MA, USA

    Erik D. Demaine

Authors
  1. John Calvin Alumbaugh
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  2. Joshua J. Daymude
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  3. Erik D. Demaine
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  4. Matthew J. Patitz
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  5. Andréa W. Richa
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Correspondence to Matthew J. Patitz .

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  1. California Institute of Technology, Pasadena, CA, USA

    Chris Thachuk

  2. Arizona State University, Tempe, AZ, USA

    Yan Liu

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Alumbaugh, J.C., Daymude, J.J., Demaine, E.D., Patitz, M.J., Richa, A.W. (2019). Simulation of Programmable Matter Systems Using Active Tile-Based Self-Assembly. In: Thachuk, C., Liu, Y. (eds) DNA Computing and Molecular Programming. DNA 2019. Lecture Notes in Computer Science(), vol 11648. Springer, Cham. https://doi.org/10.1007/978-3-030-26807-7_8

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  • DOI: https://doi.org/10.1007/978-3-030-26807-7_8

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