Abstract
A pattern for performing several DNA computations is outlined using the aqueous approach, the essence of which is writing on molecules dissolved in water. Four of the indicated computations have been carried out in wet labs in the aqueous style. As an illustration, gel photos will be exhibited that confirm the correctness of a small SAT computation. Emphasis will be placed on the aqueous approach, now in progress, to the problem of producing the set of all patterns in which knights can be placed on a 3 × 3 chessboard with no knight attacking another. Currently the writing technology used is based on molecular biology. In the future we hope that light can replace biochemistry as the writing procedure.
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References
L. Adleman, Molecular computation of solutions of combinatorial problems, Science, 266(1994)1021–1024.
G.L. Centoni, Biological methylation: selected aspects, Annual Review of Biochemistry 44 (1975), 435–451.
D. Faulhammer, A.R. Cukras, R.J. Lipton & L.F. Landweber, Proc. Nat. Acad. Sci. 97 (2000), 1385–1389.
M.R. Garey & D.S. Johnson, Computers and Intractability — A Guide to the Theory of’ NP-Completeness, W.H. Freeman, San Francisco, CA, (1979).
T. Head, Formal language theory and DNA: an analysis of the generative capacity of specific recombinant behaviors, Bull. Math. Bio. 49 (1987), 737–759.
T. Head, Circular suggestions for DNA computing, in: A. Carbone, M. Gromov & P. Pruzinkiewicz, Eds., Pattern Formation in Biology, Vision and Dynamics, World Scientific, Singapore and London, (2000), 325–335.
T. Head, Splicing systems, aqueous computing, and beyond, in: I. Antoniou, C.S. Calude & M.J. Dinneen, Eds., Unconventional Models of Computation, UMC’2K, Springer-Verlag, London, (2001).
T. Head, Writing by methylation proposed for aqueous computing, Chapter 31 in: C. Martin-Vide & V. Mitrana, Eds., Where Mathematics, Computer Science, Linguistics and Biology Meet, (2001), 353–360.
T. Head, Biomolecular realizations of a parallel architecture for solving combinatorial problems, (to appear).
T. Head, Finding bijections with DNA, (to appear).
T. Head, Gh. Paun & D. Pixton, Language theory and molecular genetics: generative mechanisms suggested by DNA recombination, a chapter in: G. Rozenberg & A. Salomaa, Eds., Handbook of Formal Languages, vol. 2, Springer, New York, 1996, pp. 295–360.
T. Head, G. Rozenberg, R.S. Bladergroen, C.K.D. Breek, P.H.M. Lommerse & H. Spaink, Computing with DNA by operating on plasmids, BioSystems 57 (2000), 87–93.
T. Head, M. Yamamura & S. Gal, Aqueous computing: writing on molecules, in: Proceedings of the Congress on Evolutionary Computing, IEEE Service Center, Piscataway, NJ, (1999), 1006–1010.
Q. Ouyang, P.D. Kaplan, S. Liu & A. Libchaber, DNA solution of the maximal clique problem, Science (1997), 446–449.
Gh. Paun, G. Rozenberg & A. Salomaa, DNA Computing — New Computing Paradigms, Springer Verlag, Berlin (1998).
P.W.K. Rothemund, A DNA and restriction enzyme implementation of Turing machines, in: DIM ACS Series in Discrete Math. & Theor. Comp. Sci., vol. 27, Amer. Math. Soc., Providence, RI, (1996).
M. Yamamura, T. Head & S. Gal, Aqueous computing-mathematical principles of molecular memory and its biomolecular implementation, Chap. 2 in: Hiroaki Kitano, Ed., Genetic Algorithms 4 (2000), 49–73. (In Japanese).
M. Yamamura, Y. Hiroto, T. Matoba, Another realization of aqueous computing with peptide nucleic acid, (This Proceedings, 2001).
H. Yoshida & A. Suyama, Solution to 3SAT by breadth first search, in: DIM ACS Series in Discrete Math. & Theor. Comp. Sci., vol. 54, Amer. Math. Soc., Providence, RI, (2000), 9–22.
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Head, T., Chen, X., Nichols, M.J., Yamamura, M., Gal, S. (2002). Aqueous Solutions of Algorithmic Problems: Emphasizing Knights on a 3 × 3. In: Jonoska, N., Seeman, N.C. (eds) DNA Computing. DNA 2001. Lecture Notes in Computer Science, vol 2340. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48017-X_18
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DOI: https://doi.org/10.1007/3-540-48017-X_18
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