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On aggregation in multiset-based self-assembly of graphs

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Abstract

We continue the formal study of multiset-based self-assembly. The process of self-assembly of graphs, where iteratively new nodes are attached to a given graph, is guided by rules operating on nodes labelled by multisets. In this way, the multisets and rules model connection points (such as “sticky ends”) and complementarity/affinity between connection points, respectively. We identify three natural ways (individual, free, and collective) to attach (aggregate) new nodes to the graph, and study the generative power of the corresponding self-assembly systems. For example, it turns out that individual aggregation can be simulated by free or collective aggregation. However, we demonstrate that, for a fixed set of connection points, collective aggregation is rather restrictive. We also give a number of results that are independent of the way that aggregation is performed.

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Acknowledgments

F. Bernardini and R. Brijder were supported by NWO, the Netherlands Organisation for Scientific Research, project 635.100.006 “VIEWS”. G. Rozenberg acknowledges support by NSF grant 0622112. M. Cavaliere and G. Franco were supported by European Research Network SegraVis. We thank the reviewers for their valuable comments on the paper.

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Authors and Affiliations

  1. Leiden Institute of Advanced Computer Science, Leiden University, Leiden, The Netherlands

    Francesco Bernardini, Robert Brijder, Hendrik Jan Hoogeboom & Grzegorz Rozenberg

  2. The Microsoft Research-University of Trento, Centre for Computational and Systems Biology (CoSBi), Trento, Italy

    Matteo Cavaliere

  3. Department of Computer Science, University of Verona, Strada Le Grazie 15, 37134, Verona, Italy

    Giuditta Franco

Authors
  1. Francesco Bernardini
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  2. Robert Brijder
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  3. Matteo Cavaliere
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  4. Giuditta Franco
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  5. Hendrik Jan Hoogeboom
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  6. Grzegorz Rozenberg
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Correspondence to Robert Brijder.

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Bernardini, F., Brijder, R., Cavaliere, M. et al. On aggregation in multiset-based self-assembly of graphs. Nat Comput 10, 17–38 (2011). https://doi.org/10.1007/s11047-010-9183-3

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