Abstract
This paper is a theoretical study of notions in combinatorics of words motivated by information being encoded as DNA strands in DNA computing. We generalize the classical notions of conjugacy and commutativity of words to incorporate the notion of an involution function, a formalization of the Watson-Crick complementarity of DNA single-strands. We define and study properties of Watson-Crick conjugate and commutative words, as well as Watson-Crick palindromes. We obtain, for example, a complete characterization of the set of all words that are not Watson-Crick palindromes. Our results hold for more general functions, such as arbitrary morphic and antimorphic involutions. They generalize classical results in combinatorics of words, while formalizing concepts meaningful for DNA computing experiments.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Adleman, L.: Towards a mathematical theory of self-assembly. Technical Report 00-722, Department of Computer Science, University of Southern California (2000)
Berstel, J., Perrin, D.: Theory of Codes. Academic Press, Orlando Florida (1985)
Blanchet-Sadri, F., Luhman, D.: Conjugacy on partial words. Theoretical Computer Science 289, 297–312 (2002)
Boyer, R., Moore, J.: A fast string searching algorithm. Communication of the ACM 20, 762–772 (1977)
Crochemore, M., Perrin, D.: Two-way string matching. Journal of Association of Computing Machinery 38, 651–675 (1991)
Crochmore, M., Rytter, W.: Jewels of Stringology. World Scientific (2003)
Crochmore, M., Mignosi, F., Restivo, A., Salemi, S.: Text compression using antidictionaries. In: Wiedermann, J., van Emde Boas, P., Nielsen, M. (eds.) ICALP 1999. LNCS, vol. 1644, pp. 261–270. Springer, Heidelberg (1999)
Daley, M., McQuillan, I.: On computational properties of template-guided DNA recombination. In: Carbone, A., Pierce, N.A. (eds.) DNA Computing. LNCS, vol. 3892, pp. 27–37. Springer, Heidelberg (2006)
de Luca, A., de Luca, A.: Pseudopalindrome closure operators in free monoids. Theoretical Computer Science 362, 282–300 (2006)
Domaratzki, M.: Hairpin structures defined by DNA trajectories. In: Mao, C., Yokomori, T. (eds.) DNA Computing. LNCS, vol. 4287, pp. 182–194. Springer, Heidelberg (2006)
Garzon, M., Phan, V., Roy, S., Neel, A.: In search of optimal codes for DNA computing. In: Mao, C., Yokomori, T. (eds.) DNA Computing. LNCS, vol. 4287, pp. 143–156. Springer, Heidelberg (2006)
Kari, L., Konstantinidis, S., Losseva, E., Wozniak, G.: Sticky-free and overhang-free DNA languages. Acta Informatica 40, 119–157 (2003)
Kari, L., Konstantinidis, S., Losseva, E., Sosik, P., Thierrin, G.: Hairpin structures in DNA words. In: Carbone, A., Pierce, N.A. (eds.) DNA Computing. LNCS, vol. 3892, pp. 158–170. Springer, Heidelberg (2006)
Kari, L., Mahalingam, K.: Involution bordered words. International Journal of Foundations of Computer Science (accepted, 2007) http://www.csd.uwo.ca/~lila/invbor.pdf
Kari, L., Mahalingam, K., Seki, S.: Language equations on Watson-Crick words, manuscript
Lothaire, M.: Combinatorics of Words. Cambridge University Press, Cambridge (1997)
Marathe, A., Condon, A., Corn, R.: On combinatorial DNA word design. In: Winfree, E., Gifford, D. (eds.) Proc. of DNA Based Computers 5, DIMACS Series in Discrete Math. and Theoretical Comp. Sci. pp. 75–89 (1999)
Margaritis, D., Skiena, S.: Reconstructing strings from substrings in rounds. In: Proceedings of the 36th Annual Symposium on Foundations of Computer Science, pp. 613–620 (1995)
Shyr, H.J.: Free Monoids and Languages. Hon Min Book Company (2001)
Soloveichik, D., Winfree, E.: Complexity of compact proofreading for self-assembled patterns. In: Carbone, A., Pierce, N.A. (eds.) DNA Computing. LNCS, vol. 3892, pp. 305–324. Springer, Heidelberg (2006)
Storer, J.A.: Data Compression: Methods and Theory. Computer Science Press, Rockville (1998)
Yu, S.S.: d-minimal languages. Discrete Applied Mathematics 89, 243–262 (1998)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kari, L., Mahalingam, K. (2008). Watson-Crick Conjugate and Commutative Words. In: Garzon, M.H., Yan, H. (eds) DNA Computing. DNA 2007. Lecture Notes in Computer Science, vol 4848. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77962-9_29
Download citation
DOI: https://doi.org/10.1007/978-3-540-77962-9_29
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-77961-2
Online ISBN: 978-3-540-77962-9
eBook Packages: Computer ScienceComputer Science (R0)