Difference between revisions of "Open Problems"
(→References) |
|||
| Line 9: | Line 9: | ||
<br> | <br> | ||
3) In <ref name = IUSA /> Doty et al. showed that the aTAM is [[Intrinsic Universality | intrinsically universal]] for itself, but for [[Directed Tile Assembly Systems | directed]] systems the intrinsically universal tile set fundamentally relies on nondeterminism. Is the class of directed [[Abstract Tile Assembly Model (aTAM) | aTAM]] systems intrinsically universal for itself? | 3) In <ref name = IUSA /> Doty et al. showed that the aTAM is [[Intrinsic Universality | intrinsically universal]] for itself, but for [[Directed Tile Assembly Systems | directed]] systems the intrinsically universal tile set fundamentally relies on nondeterminism. Is the class of directed [[Abstract Tile Assembly Model (aTAM) | aTAM]] systems intrinsically universal for itself? | ||
| + | <br> | ||
| + | <br> | ||
| + | 4) Is the [[STAM]] [[Intrinsic Universality | intrinsically universal]] for itself? | ||
| + | <br> | ||
| + | <br> | ||
| + | 5) Is the class of [[Abstract Tile Assembly Model (aTAM) | aTAM]] systems at temperature 1 [[Intrinsic Universality | intrinsically universal]] for itself? | ||
| + | <br> | ||
| + | <br> | ||
| + | 6) In his 1998 thesis <ref name=Winf98 />, Winfree introduced both the [[Abstract Tile Assembly Model (aTAM) | aTAM]] and its more practical counterpart the [[Kinetic Tile Assembly Model (kTAM) | kTAM]. Currently, the 2HAM does not have a more realistic counterpart. Formulate a "k2HAM" model which takes into account the size of assemblies binding together (the bigger the assemblies the less likely it is they will bind together) and the lack of rigidity when assemblies come together. | ||
Revision as of 12:07, 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.
2) In [4], Doty et al. introduced a model known as the fuzzy temperature model and showed that in this model n by n squares could efficiently self-assemble. Can systems in this model also perform general computation?
3) In [5] Doty et al. showed that the aTAM is intrinsically universal for itself, but for directed systems the intrinsically universal tile set fundamentally relies on nondeterminism. Is the class of directed aTAM systems intrinsically universal for itself?
4) Is the STAM intrinsically universal for itself?
5) Is the class of aTAM systems at temperature 1 intrinsically universal for itself?
6) In his 1998 thesis [1], Winfree introduced both the aTAM and its more practical counterpart the [[Kinetic Tile Assembly Model (kTAM) | kTAM]. Currently, the 2HAM does not have a more realistic counterpart. Formulate a "k2HAM" model which takes into account the size of assemblies binding together (the bigger the assemblies the less likely it is they will bind together) and the lack of rigidity when assemblies come together.
References
- ↑ 1.0 1.1
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
- ↑
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
- BibtexAuthor : 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
- ↑
David Doty, Jack H. Lutz, Matthew J. Patitz, Robert T. Schweller, Scott M. Summers, Damien Woods - The tile assembly model is intrinsically universal
- Proceedings of the 53rd Annual IEEE Symposium on Foundations of Computer Science ,2012
- BibtexAuthor : David Doty, Jack H. Lutz, Matthew J. Patitz, Robert T. Schweller, Scott M. Summers, Damien Woods
Title : The tile assembly model is intrinsically universal
In : Proceedings of the 53rd Annual IEEE Symposium on Foundations of Computer Science -
Address :
Date : 2012
