Abstract
The set of all sequences that are generated by a biomolecular protocol forms a language over the four letter alphabet Δ={A,G,C,T}. This alphabet is associated with a natural involution mapping θ, A↦T and G↦C which is an antimorphism of Δ*. In order to avoid undesirable Watson-Crick bonds between the words (undesirable hybridization), the language has to satisfy certain coding properties. In this paper we build upon an earlier initiated study and give general methods for obtaining sets of code words with the same properties. We show that some of these code words have enough entropy to encode {0,1}* in a symbol-to-symbol mapping.
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References
Adler, R.L., Coppersmith, D., Hassner, M.: Algorithms for sliding block codes -an application of symbolic dynamics to information theory. IEEE Trans. Inform. Theory 29, 5–22 (1983)
Arita, M., Kobayashi, S.: DNA sequence design using templates. New Generation Comput. 20(3), 263–277 (2002), Available as a sample paper at http://www.ohmsha.co.jp/ngc/index.htm
Baum, E.B.: DNA Sequences useful for computation unpublished article (1996), available at http://www.neci.nj.nec.com/homepages/eric/seq.ps
Braich, R.S., et al.: Solution of a 20-variable 3-SAT problem on a DNA computer. Science 296, 499–502 (2002)
Berstel, J., Perrin, D.: Theory of codes. Academis Press, Inc., Orlando (1985)
Lind, D., Marcus, B.: An introduction to Symbolic Dynamics and Coding. Cambridge University Press, Inc., Cambridge (1999)
Deaton, R., et al.: A PCR-based protocol for in vitro selection of non-crosshybridizing oligonucleotides. In: Hagiya, M., Ohuchi, A. (eds.) DNA 2002. LNCS, vol. 2568, pp. 196–204. Springer, Heidelberg (2003)
Deaton, R., et al.: A DNA based implementation of an evolutionary search for good encodings for DNA computation. In: Proc. IEEE Conference on Evolutionary Computation ICEC 1997, pp. 267–271 (1997)
Faulhammer, D., Cukras, A.R., Lipton, R.J., Landweber, L.F.: Molecular Computation: RNA solutions to chess problems. Proceedings of the National Academy of Sciences 97(4), 1385–1389 (2000)
Feldkamp, U., Saghafi, S., Rauhe, H.: DNASequenceGenerator - A program for the construction of DNA sequences. In: Jonoska, N., Seeman, N.C. (eds.) DNA 2001. LNCS, vol. 2340, pp. 23–32. Springer, Heidelberg (2002)
Garzon, M., Deaton, R., Reanult, D.: Virtual test tubes: a new methodology for computing. In: Proc. 7th. Int. Symposium on String Processing and Information retrieval, A Corun̆a, Spain, pp. 116–121. IEEE Computing Society Press, Los Alamitos (2000)
Head, T.: Relativised code properties and multi-tube DNA dictionaries in Finite vs. Infinite. In: Calude, C., Paun, G. (eds.), pp. 175–186. Springer, Heidelberg (2000)
Hussini, S., Kari, L., Konstantinidis, S.: Coding properties of DNA languages. In: Jonoska, N., Seeman, N.C. (eds.) DNA 2001. LNCS, vol. 2340, pp. 57–69. Springer, Heidelberg (2002)
Jonoska, N., Mahalingam, K.: Languages of DNA based code words Preliminary. In: Proceedings of the 9th International Meeting on DNA Based Computers, Madison, Wisconsin, June 1-4, pp. 58–68 (2003)
Jonoska, N., Kephart, D., Mahalingam, K.: Generating DNA code words. Congressus Numernatium 156, 99–110 (2002)
Kari, L., Konstantinidis, S., Losseva, E., Wozniak, G.: Sticky-free and overhang-free DNA languages (preprint)
Keane, M.S.: Ergodic theory an subshifts of finite type. In: Edford, T., et al. (eds.) Ergodic theory, symbolic dynamics and hyperbolic spaces, pp. 35–70. Oxford Univ. Press, Oxford (1991)
Li, Z.: Construct DNA code words using backtrack algorithm (preprint)
Liu, Q., et al.: DNA computing on surfaces. Nature 403, 175–179 (2000)
Marathe, A., Condon, A.E., Corn, R.M.: On combinatorial word design. In: Preliminary Preproceedings of the 5th International Meeting on DNA Based Computers, Boston, pp. 75–88 (1999)
Paun, G., Rozenberg, G., Salomaa, A.: DNA Computing, New computing paradigms. Springer, Heidelberg (1998)
Ruben, A.J., Freeland, S.J., Landweber, L.F.: PUNCH: An evolutionary algorithm for optimizing bit set selection. In: Jonoska, N., Seeman, N.C. (eds.) DNA 2001. LNCS, vol. 2340, pp. 150–160. Springer, Heidelberg (2002)
Seeman, N.C.: De Novo design of sequences for nucleic acid structural engineering. J. of Biomolecular Structure & Dynamics 8(3), 573–581 (1990)
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Jonoska, N., Mahalingam, K. (2003). Methods for Constructing Coded DNA Languages. In: Jonoska, N., Păun, G., Rozenberg, G. (eds) Aspects of Molecular Computing. Lecture Notes in Computer Science, vol 2950. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24635-0_17
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DOI: https://doi.org/10.1007/978-3-540-24635-0_17
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