Limitations of self-assembly at temperature 1

Theoretical Computer Science

Volumn 412, Issue 1-2, 2011, Pages 145-158

  Doty, David ^a   Patitz, Matthew J ^b   Summers, Scott M ^c  

^a California Institute of Technology   (United States)

^b UNIVERSITY OF TEXAS PAN AMERICAN   (United States)

^c UNIVERSITY OF WISCONSIN PLATTEVILLE   (United States)

Author keywords

General purpose computation; Semilinear set; Temperature 1; Tile self assembly

Indexed keywords

ASSEMBLY; CUSTOMER SATISFACTION;

ASSEMBLY SYSTEMS; GENERAL-PURPOSE COMPUTATIONS; NATURAL CONDITIONS; SELF-SIMILAR FRACTALS; SEMI-LINEAR SETS;

SELF ASSEMBLY;

EID: 80053164481     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.tcs.2010.08.023     Document Type: Conference Paper

References (19)

1. Leonard M. Adleman, Jarkko Kari, Lila Kari, Dustin Reishus, Petr Sosík, The undecidability of the infinite ribbon problem: implications for computing by self-assembly, SIAM Journal on Computing 38 (6) (2009) 2356-2381.
2. David Doty, Randomized self-assembly for exact shapes, in: Proceedings of the Fiftieth IEEE Conference on Foundations of Computer Science, FOCS, 2009.
3. David Doty, Xiaoyang Gu, Jack H. Lutz, Elvira Mayordomo, Philippe Moser, Zeta-Dimension, in: Proceedings of the Thirtieth International Symposium on Mathematical Foundations of Computer Science, Springer-Verlag, 2005, pp. 283-294.
4. Yunhui Fu, Robert T. Schweller, Temperature 1 self-assembly: deterministic assembly in3D and probabilistic assembly in 2D, Tech. Report 0912.0027, Computing Research Repository, 2009.
5. Oscar H. Ibarra, Reversal-bounded multicounter machines and their decision problems, Journal of the ACM 25 (1) (1978) 116-133.
6. Ming-Yang Kao, Robert T. Schweller, Randomized self-assembly for approximate shapes, in: Luca Aceto, Ivan Damgård, Leslie Ann Goldberg, Magns M. Halldrsson, Anna Inglfsdttir, Igor Walukiewicz (Eds.), International Colloqium on Automata, Languages, and Programming, ICALP, in: Lecture Notes in Computer Science, vol. 5125, Springer, 2008, pp. 370-384.
7. James I. Lathrop, Jack H. Lutz, Scott M. Summers, Strict self-assembly of discrete Sierpinski triangles, Theoretical Computer Science 410 (2009) 384-405.
8. Ján Maňuch, Ladislav Stacho, Christine Stoll, Two lower bounds for self-assemblies at temperature 1, in: Bioinformatics and Biomedical Engineering, 2009. ICBBE 2009. 3rd International Conference on, June 2009, pp. 1-4.
9. Ján Maňuch, Ladislav Stacho, Christine Stoll, Two lower bounds for self-assemblies at temperature 1, in: SAC'09: Proceedings of the 2009 ACM Symposium on Applied Computing, ACM, New York, NY, USA, 2009, pp. 808-809.
10. Matthew J. Patitz, Scott M. Summers, Self-assembly of decidable sets, Natural Computing (in press).
11. Mojżesz Presburger, Über die vollständigkeit eines gewissen systems der arithmetik ganzer zahlen, welchem die Addition als einzige Operation hervortritt. Compte Rendus du I. Congrks des Mathematiciens des pays Slavs, Warsaw, 1930, pp. 92-101.
12. Paul W.K. Rothemund, Theory and experiments in algorithmic self-assembly, Ph.D. Thesis, University of Southern California, December 2001.
13. Paul W.K. Rothemund, Erik Winfree, The program-size complexity of self-assembled squares (extended abstract), in: STOC'00: Proceedings of the thirty-second annual ACM Symposium on Theory of Computing, ACM, New York, NY, USA, 2000, pp. 459-468.
14. Paul W.K. Rothemund, Nick Papadakis, Erik Winfree, Algorithmic self-assembly of DNA Sierpinski triangles, PLoS Biology 2 (12) (2004) 2041-2053.
15. Nadrian C. Seeman, Nucleic-acid junctions and lattices, Journal of Theoretical Biology 99 (1982) 237-247.
16. Ryan Stansifer, Presburger's article on integer arithmetic: Remarks and translation, Tech. Report TR84-639, Cornell University, Computer Science Department, September, 1984.
17. Hao Wang, Proving theorems by pattern recognition - II, The Bell System Technical Journal XL (1) (1961) 1-41.
18. Hao Wang, Dominoes and the AEA case of the decision problem, in: Proceedings of the Symposium on Mathematical Theory of Automata (New York, 1962), Polytechnic Press of Polytechnic Inst. of Brooklyn, Brooklyn, N.Y., 1963, pp. 23-55.
19. Erik Winfree, Algorithmic self-assembly of DNA, Ph.D. Thesis, California Institute of Technology, June, 1998.