Negative Interactions in Irreversible Self-assembly

  • David Doty
  • Lila Kari
  • Benoît Masson
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6518)


This paper explores the use of negative (i.e., repulsive) interactions in the abstract Tile Assembly Model defined by Winfree. Winfree in his Ph.D. thesis postulated negative interactions to be physically plausible, and Reif, Sahu, and Yin studied them in the context of reversible attachment operations. We investigate the power of negative interactions with irreversible attachments, and we achieve two main results. Our first result is an impossibility theorem: after t steps of assembly, Ω(t) tiles will be forever bound to an assembly, unable to detach. Thus negative glue strengths do not afford unlimited power to reuse tiles. Our second result is a positive one: we construct a set of tiles that can simulate an s-space-bounded, t-time-bounded Turing machine, while ensuring that no intermediate assembly grows larger than O(s), rather than O(s ·t) as required by the standard Turing machine simulation with tiles.


Turing Machine Impossibility Result Tile Type Intermediate Assembly Tape Head 
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  1. 1.
    Aggarwal, G., Cheng, Q., Goldwasser, M.H., Kao, M.-Y., Moisset de Espanés, P., Schweller, R.T.: Complexities for generalized models of self-assembly. SIAM Journal on Computing 34, 1493–1515 (2005); Preliminary version appeared in SODA 2004 MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Doty, D., Lutz, J.H., Patitz, M.J., Summers, S.M., Woods, D.: Random number selection in self-assembly. In: Calude, C.S., Costa, J.F., Dershowitz, N., Freire, E., Rozenberg, G. (eds.) UC 2009. LNCS, vol. 5715, pp. 143–157. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  3. 3.
    Doty, D., Lutz, J.H., Patitz, M.J., Summers, S.M., Woods, D.: Intrinsic universality in self-assembly. In: STACS 2010: Proceedings of the 27th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), vol. 5, pp. 275–286 (2010)Google Scholar
  4. 4.
    Reif, J.H., Sahu, S., Yin, P.: Complexity of graph self-assembly in accretive systems and self-destructible systems. In: Carbone, A., Pierce, N.A. (eds.) DNA 11. LNCS, vol. 3892, pp. 257–274. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  5. 5.
    Rothemund, P.W.K., Winfree, E.: The program-size complexity of self-assembled squares (extended abstract). In: STOC 2000: Proceedings of the Thirty-Second Annual ACM Symposium on Theory of Computing, pp. 459–468 (2000)Google Scholar
  6. 6.
    Schoen, R., Yau, S.-T.: On the positive mass conjecture in general relativity. Communications in Mathematical Physics 65(45), 45–76 (1979)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Seeman, N.C.: Nucleic-acid junctions and lattices. Journal of Theoretical Biology 99, 237–247 (1982)CrossRefGoogle Scholar
  8. 8.
    Soloveichik, D., Cook, M., Winfree, E., Bruck, J.: Computation with finite stochastic chemical reaction networks. Natural Computing 7(4), 615–633 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Wang, H.: Proving theorems by pattern recognition – II. The Bell System Technical Journal XL(1), 1–41 (1961)CrossRefGoogle Scholar
  10. 10.
    Winfree, E.: Algorithmic Self-Assembly of DNA. PhD thesis, California Institute of Technology (June 1998)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • David Doty
    • 1
  • Lila Kari
    • 1
  • Benoît Masson
    • 2
  1. 1.Dept. of Computer ScienceU. of West. OntarioLondonCanada
  2. 2.IRISA (INRIA)RennesFrance

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