Abstract
In a DNA computation a select operation is used to separate DNA molecules with different sequences. The implementation of the select operation requires specialized hardware and non-standard modification of DNA molecules by adding e.g., magnetic beads to a primer sequence or using other methods to separate DNA in solution. In this paper we consider DNA computations which use enzymatic reactions and secondary structure formation to perform computations.We show that it is possible to implement an efficient (exponential-time) probabilistic algorithm to solve instances of the satisfiability problem on circular single stranded DNA.
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References
L.M. Adleman. Molecular computation of solutions to combinatorial problems. Science, 266:1021–1024, 1994.
F.M. Ausubel, R. Brent, R.E. Kingston, D.D. Moore, J.G. Seidman, J.A. Smith, and K. Struhl, editors. Current Protocols in Molecular Biology. Wiley and Sons, 2001.
E. Bach, A. Condon, E. Glaser, and C. Tanguay. DNA models and algorithms for NP-complete problems. In Proc. of 11th Conference on Computational Complexity, pages 290–299. IEEE Computer Society Press, 1996.
R.S. Braich, N. Chelyapof, C. Johnson, P.W.K. Rothemund, and L.M. Adleman. Solution of a 20-variable 3-SAT problem on a DNA computer. Science, 96:478–479, 2002.
K. Chen and V. Ramachandran. A space-efficient randomized DNA algorithm for k-sat. In A. Condon, editor, Sixth International Workshop on DNA-based Computers, volume 2054 of LNCS. Springer-Verlag, 2001.
E. Dantsin, A. Goerdt, Hirsch E.A., R. Kannan, J. Kleinberg, C. Papadimitriu, P. Raghavan, and U. Schöning. Deterministic local search decides k-SAT in time (2-2/(k +1))n. TCS, in press, 2002.
S. Diaz, J. L. Esteban, and M. A Ogihara. A DNA-based random walk method for solving k-sat. In A. Condon, editor, Sixth International Workshop on DNA-based Computers, volume 2504 of LNCS. Springer-Verlag, 2001.
A. G. Frutos, Q. Liu, A. J. Thiel, A. M. Sanner, A. E. Condon., L. M. Smith, and R. M. Corn. Demonstration of a word design strategy for DNA computing on surfaces. Nucleic Acids Res, 25(23):4748–4757, 1997.
T. Hofmeister, U. Schöning, R. Schuler, and O. Watanabe. A probabilistic 3-SAT algorithm further improved. In Proceedings 19th Symposium on Theoretical Aspects of Computer Science, volume 2285 of LNCS, pages 192–203. Springer-Verlag, 2002.
Q. Liu, L. Wang, A. G. Frutos, A. E. Condon, R. M. Corn, and L. M. Smith. DNA computing on surfaces. Nature, 403:175–179, 2000.
J. S. McCaskill. Optically programming DNA computing in microflow reactors. Biosystems, 59:125–138, 2001.
K. Sakamoto, H. Gouzu, K. Komiya, D. Kiga, S. Yokoyama, T. Yokomori, and M. Hagiya. Molecular computation by DNA hairpin formation. Science, 288:1223–1226, 2000.
U. Schöning. A probabilistic algorithm for k-SAT and constraint satisfaction problems. In Porc. 40th FOCS, pages 410–414. ACM, 1999.
L. Wang, J. G. Hall, M. Lu, Q Liu, and L. M. Smith. A DNA computing readout operation based on structure-specific cleavage. Nature Biotech., 19:1053–1059, 2001.
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Hug, H., Schuler, R. (2003). Implementation of a Random Walk Method for Solving 3-SAT on Circular DNA Molecules. In: Hagiya, M., Ohuchi, A. (eds) DNA Computing. DNA 2002. Lecture Notes in Computer Science, vol 2568. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36440-4_12
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DOI: https://doi.org/10.1007/3-540-36440-4_12
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