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Intrinsic Universality in Self-Assembly

  • Reference work entry
  • First Online:
Encyclopedia of Algorithms

  • 225 Accesses

Years and Authors of Summarized Original Work

  • 2012; Doty, Lutz, Patitz, Schweller, Summers, Woods

  • 2013; Demaine, Patitz, Rogers, Schweller, Summers, Woods

  • 2014; Meunier, Patitz, Summers, Theyssier, Winslow, Woods

  • 2014; Demaine, Demaine, Fekete, Patitz, Schweller, Winslow, Woods

Problem Definition

Algorithmic self-assembly [11] is the idea that small self-assembling molecules can compute as they grow structures. It gives programmers a set of theoretical models in which to specify and design target structures while trying to optimize resources such as number of molecule types or even construction time. The abstract Tile Assembly Model [11] is one such model. An instance of the model is called a tile assembly system and is a triple \(\mathcal{T} = (T,\sigma ,\tau )\) consisting of a finite set T of square tiles, a seed assembly \(\sigma\) (one or more tiles stuck together), and a temperature τ ∈ { 1, 2, 3, …}, as shown in Fig. 1a. Each side of a square tile has a glue (or color) gwhich...

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Recommended Reading

  1. Cook M, Fu Y, Schweller RT (2011) Temperature 1 self-assembly: deterministic assembly in 3D and probabilistic assembly in 2D. In: SODA 2011: Proceedings of the 22nd annual ACM-SIAM symposium on discrete algorithms, San Francisco. SIAM, pp 570–589

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  2. Delorme M, Mazoyer J, Ollinger N, Theyssier G (2011) Bulking II: classifications of cellular automata. Theor Comput Sci 412(30):3881–3905. DOI10.1016/j.tcs.2011.02.024

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  3. Demaine ED, Patitz MJ, Rogers TA, Schweller RT, Summers SM, Woods D (2013) The two-handed tile assembly model is not intrinsically universal. In: ICALP: Proceedings of the 40th international colloquium on automata, languages and programming, Part 1, Riga. LNCS, vol 7965. Springer, pp 400–412. arxiv preprint arXiv:1306.6710 [cs.CG]

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  4. Demaine ED, Demaine ML, Fekete SP, Patitz MJ, Schweller RT, Winslow A, Woods D (2014) One tile to rule them all: simulating any tile assembly system with a single universal tile. In: ICALP: Proceedings of the 41st international colloquium on automata, languages, and programming, Copenhagen. LNCS, vol 8572. Springer, pp 368–379. arxiv preprint arXiv:1212.4756 [cs.DS]

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  5. Doty D, Lutz JH, Patitz MJ, Schweller RT, Summers SM, Woods D (2012) The tile assembly model is intrinsically universal. In: FOCS: Proceedings of the 53rd annual IEEE symposium on foundations of computer science, New Brunswick, pp 439–446. DOI10.1109/FOCS.2012.76

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  6. Fochtman T, Hendricks J, Padilla JE, Patitz MJ, Rogers TA (2014) Signal transmission across tile assemblies: 3D static tiles simulate active self-assembly by 2D signal-passing tiles. Nat Comput 14(2):251–264

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  7. Gilbert O, Hendricks J, Patitz MJ, Rogers TA (2015) Computing in continuous space with self-assembling polygonal tiles. Tech. rep., arxiv preprint arXiv:1503.00327 [cs.CG]

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  8. Hendricks J, Patitz MJ, Rogers TA (2015) The simulation powers and limitations of higher temperature hierarchical self-assembly systems. In: MCU: Proceedings of the 7th international conference on machines, computations and universality, North Cyprus, to appear. Tech. rep., arXiv arXiv:1503.04502

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  9. Jonoska N, Karpenko D (2014) Active tile self-assembly, part 1: universality at temperature 1. Int J Found Comput Sci 25:141–163. doi:10.1142/S0129054114500087

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  10. Meunier PE, Patitz MJ, Summers SM, Theyssier G, Winslow A, Woods D (2014) Intrinsic universality in tile self-assembly requires cooperation. In: SODA: Proceedings of the ACM-SIAM symposium on discrete algorithms, Portland, pp 752–771. arxiv preprint arXiv:1304.1679 [cs.CC]

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  11. Winfree E (1998) Algorithmic self-assembly of DNA. PhD thesis, California Institute of Technology

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  12. Woods D (2015) Intrinsic universality and the computational power of self-assembly. Philos Trans R Soc A Math Phys Eng Sci 373(2046):20140214

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  13. Woods D, Chen HL, Goodfriend S, Dabby N, Winfree E, Yin P (2013) Active self-assembly of algorithmic shapes and patterns in polylogarithmic time. In: ITCS: Proceedings of the 4th conference on innovations in theoretical computer science, Berkeley. ACM, pp 353–354. arxiv preprint arXiv:1301.2626 [cs.DS]

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Acknowledgements

A warm thanks to all of my coauthors on this topic. The author is supported by NSF grants 0832824, 1317694, CCF-1219274, and CCF-1162589.

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Authors and Affiliations

  1. Computer Science, California Institute of Technology, 91125, Pasadena, CA, USA

    Damien Woods

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  1. Damien Woods
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Correspondence to Damien Woods .

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  1. Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL, USA

    Ming-Yang Kao

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Woods, D. (2016). Intrinsic Universality in Self-Assembly. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_661

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