Difference between revisions of "Open Problems"
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| − | + | The following are a list of open problems in self-assembly: | |
| + | <br> | ||
| + | 1) In his 1998 thesis <ref name=Winf98 />, Winfree showed that the class of directed [[Abstract Tile Assembly Model (aTAM) | aTAM]] systems at temperature 2 is computationally universal, and in <ref name=CooFuSch11/> 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 <ref name=jLSAT1 /> Doty, Patitz, and Summers provide deep insights into this question. | ||
| + | |||
| + | ==References== | ||
| + | <references> | ||
| + | |||
| + | <ref name =Winf98><bibtex> | ||
| + | @phdthesis{Winf98, | ||
| + | author = "Erik Winfree", | ||
| + | title = "Algorithmic Self-Assembly of DNA", | ||
| + | school = "California Institute of Technology", | ||
| + | year = "1998", | ||
| + | month = "June", | ||
| + | } | ||
| + | </bibtex></ref> | ||
| + | |||
| + | <ref name =jLSAT1><bibtex> | ||
| + | @article{jLSAT1, | ||
| + | author = "David Doty and Matthew J. Patitz and Scott M. Summers", | ||
| + | title = "Limitations of Self-Assembly at Temperature 1", | ||
| + | journal = "Theoretical Computer Science", | ||
| + | volume = "412", | ||
| + | issue = "1-2", | ||
| + | pages="145-158", | ||
| + | year = "2011" | ||
| + | } | ||
| + | </bibtex></ref> | ||
| + | |||
| + | <ref name =CooFuSch11><bibtex> | ||
| + | @inproceedings{CooFuSch11, | ||
| + | author = "Matthew Cook and Yunhui Fu and Robert T. Schweller", | ||
| + | title = "Temperature 1 Self-Assembly: Deterministic Assembly in 3{D} and Probabilistic Assembly in 2{D}", | ||
| + | year = 2011, | ||
| + | booktitle = {SODA 2011: Proceedings of the 22nd Annual ACM-SIAM Symposium on Discrete Algorithms}, | ||
| + | publisher = {SIAM}, | ||
| + | } | ||
| + | </bibtex></ref> | ||
| + | |||
| + | </references> | ||
[[Category: self-assembly]] | [[Category: self-assembly]] | ||
Revision as of 10:14, 27 May 2014
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.
References
- ↑
Erik Winfree - Algorithmic Self-Assembly of DNA
- Ph.D. Thesis, California Institute of Technology , June 1998
- BibtexAuthor : Erik Winfree
Title : Algorithmic Self-Assembly of DNA
In : Ph.D. Thesis, California Institute of Technology -
Address :
Date : June 1998
- ↑
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
- BibtexAuthor : 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
- ↑
David Doty, Matthew J. Patitz, Scott M. Summers - Limitations of Self-Assembly at Temperature 1
- Theoretical Computer Science 412:145-158,2011
- BibtexAuthor : David Doty, Matthew J. Patitz, Scott M. Summers
Title : Limitations of Self-Assembly at Temperature 1
In : Theoretical Computer Science -
Address :
Date : 2011
