Abstract
We define the hairpin reduction as the inverse operation of a formal operation on words and languages suggested by DNA biochemistry, namely the hairpin completion, introduced in [3]. We settle the closure properties of some classes in the Chomsky hierarchy as well as some complexity classes under the non-iterated version of the hairpin reduction, in comparison with the hairpin completion. Then an algorithm that decides whether or not a regular language coincides with its primitive hairpin root is presented. Finally, we discuss a cubic time algorithm for computing the common ancestors of two given words. This algorithm may be used also for computing the closest or farthest primitive hairpin root of a given word.
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Bottoni, P., Labella, A., Manca, V., Mitrana, V.: Superposition based on Watson-Crick-like complementarity. Theory of Computing Systems 39(4), 503–524 (2006)
Castellanos, J., Mitrana, V.: Some remarks on hairpin and loop languages. In: Ito, M., Păun, G., Yu, S. (eds.) Words, Semigroups, and Translations, pp. 47–59. World Scientific, Singapore (2001)
Cheptea, D., Martin-Vide, C., Mitrana, V.: A new operation on words suggested by DNA biochemistry: hairpin completion. In: Proc. Transgressive Computing, pp. 216–228 (2006)
Deaton, R., Murphy, R., Garzon, M., Franceschetti, D.R., Stevens, S.E.: Good encodings for DNA-based solutions to combinatorial problems. In: Landweber, L.F., Baum, E (eds). Proc. of DNA-based computers II, DIMACS Series, vol. 44, pp. 247–258 (1998)
Galil, Z., Seiferas, J.: Time-space optimal string matching. Journal of Computer and System Sciences 26, 280–294 (1983)
Garzon, M., Deaton, R., Neathery, P., Murphy, R.C., Franceschetti, D.R., Stevens, E.: On the encoding problem for DNA computing. In: The Third DIMACS Workshop on DNA-Based Computing, Univ. of Pennsylvania, pp. 230–237 (1997)
Garzon, M., Deaton, R., Nino, L.F., Stevens, Jr S.E., Wittner, M.: Genome encoding for DNA computing. In: Proc. Third Genetic Programming Conference, Madison, MI, pp. 684–690 (1998)
Knuth, D.E., Morris, J.H., Pratt, V.R.: Fast pattern matching in strings. SIAM Journal of Computing 6, 323–350 (1977)
Kari, L., Konstantinidis, S., Sosik, P., Thierrin, G.: On hairpin-free words and languages. In: De Felice, C., Restivo, A. (eds.) DLT 2005. LNCS, vol. 3572, pp. 296–307. Springer, Berlin (2005)
Manea, F., Martín-Vide, C., Mitrana, V.: On some algorithmic problems regarding the hairpin completion (submitted)
Păun, G., Rozenberg, G., Salomaa, A.: DNA Computing. New Computing Paradigms, Springer-Verlag, Berlin, 1998, Tokyo (1999)
Păun, G., Rozenberg, G., Yokomori, T.: Hairpin languages. Intern. J. Found. Comp. Sci. 12(6), 837–847 (2001)
Rozenberg, G., Salomaa, A. (eds.): Handbook of Formal Languages, vol. 3. Springer, Heidelberg (1997)
Sakamoto, K., Gouzu, H., Komiya, K., Kiga, D., Yokoyama, S., Yokomori, T., Hagiya, M.: Molecular computation by DNA hairpin formation. Science 288, 1223–1226 (2000)
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Manea, F., Mitrana, V. (2007). Hairpin Completion Versus Hairpin Reduction. In: Cooper, S.B., Löwe, B., Sorbi, A. (eds) Computation and Logic in the Real World. CiE 2007. Lecture Notes in Computer Science, vol 4497. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73001-9_55
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DOI: https://doi.org/10.1007/978-3-540-73001-9_55
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