Open Problems

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The following are a list of open problems in self-assembly:
1) In his 1998 thesis [1], Winfree showed that the class of directed aTAM systems at temperature 2 is computationally universal, and in [2] Cook et al. showed that undirected temperature 1 aTAM systems could perform computations with a given amount of certainty and that in 2 planes directed aTAM temperature 1 systems were computationally universal. Is the class of directed aTAM systems at temperature 1 in the plane computationally universal? In [3] Doty, Patitz, and Summers provide deep insights into this question.
2) In [4], Doty et al.


References

  1. Erik Winfree - Algorithmic Self-Assembly of DNA
    Ph.D. Thesis, California Institute of Technology , June 1998
    Bibtex
    Author : Erik Winfree
    Title : Algorithmic Self-Assembly of DNA
    In : Ph.D. Thesis, California Institute of Technology -
    Address :
    Date : June 1998
  2. Matthew Cook, Yunhui Fu, Robert T. Schweller - Temperature 1 Self-Assembly: Deterministic Assembly in 3{D} and Probabilistic Assembly in 2{D}
    SODA 2011: Proceedings of the 22nd Annual ACM-SIAM Symposium on Discrete Algorithms ,2011
    Bibtex
    Author : Matthew Cook, Yunhui Fu, Robert T. Schweller
    Title : Temperature 1 Self-Assembly: Deterministic Assembly in 3{D} and Probabilistic Assembly in 2{D}
    In : SODA 2011: Proceedings of the 22nd Annual ACM-SIAM Symposium on Discrete Algorithms -
    Address :
    Date : 2011
  3. David Doty, Matthew J. Patitz, Scott M. Summers - Limitations of Self-Assembly at Temperature 1
    Theoretical Computer Science 412:145-158,2011
    Bibtex
    Author : David Doty, Matthew J. Patitz, Scott M. Summers
    Title : Limitations of Self-Assembly at Temperature 1
    In : Theoretical Computer Science -
    Address :
    Date : 2011
  4. David Doty, Matthew J. Patitz, Dustin Reishus, Robert T. Schweller, Scott M. Summers - Strong Fault-Tolerance for Self-Assembly with Fuzzy Temperature
    Proceedings of the 51st Annual IEEE Symposium on Foundations of Computer Science (FOCS 2010) pp. 417--426,2010
    Bibtex
    Author : David Doty, Matthew J. Patitz, Dustin Reishus, Robert T. Schweller, Scott M. Summers
    Title : Strong Fault-Tolerance for Self-Assembly with Fuzzy Temperature
    In : Proceedings of the 51st Annual IEEE Symposium on Foundations of Computer Science (FOCS 2010) -
    Address :
    Date : 2010