Abstract
This work concerns formal descriptions of DNA code properties and related (un)decidability questions. This line of research allows us to give a property as input to an algorithm, in addition to any regular language, which can then answer questions about the language and the property. Here we define DNA code properties via transducers and show that this method is strictly more expressive than that of regular trajectories, without sacrificing the efficiency of deciding the satisfaction question. We also show that the maximality question can be undecidable. Our undecidability results hold not only for the fixed DNA involution but also for any fixed antimorphic permutation. Moreover, we also show the undecidability of the antimorphic version of the Post correspondence problem, for any fixed antimorphic permutation.
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References
Allauzen, C., Mohri, M.: Efficient algorithms for testing the twins property. J. Autom. Lang. Comb. 8(2), 117–144 (2003)
Baum, E.: DNA sequences useful for computation. In: 2nd DIMACS Workshop on DNA-based Computers, pp. 122–127. Princeton University (1996)
Berstel, J.: Transductions and Context-Free Languages. B.G. Teubner, Stuttgart (1979)
Berstel, J., Perrin, D., Reutenauer, C.: Codes and Automata. Cambridge University Press, New York (2009)
Domaratzki, M.: Trajectory-based codes. Acta Informatica 40, 491–527 (2004)
Domaratzki, M.: Bond-free DNA language classes. Nat. Comput. 6, 371–402 (2007)
Domaratzki, M., Salomaa, K.: Codes defined by multiple sets of trajectories. Theor. Comput. Sci. 366, 182–193 (2006)
Dudzinski, K., Konstantinidis, S.: Formal descriptions of code properties: decidability, complexity, implementation. IJFCS 23(1), 67–85 (2012)
FAdo: Tools for formal languages manipulation. http://fado.dcc.fc.up.pt/. Accessed February 2015
Fan, C.M., Wang, J.T., Huang, C.C.: Some properties of involution binary relations. Acta Informatica (2014). doi:10.1007/s00236-014-0208-8
Genova, D., Mahalingam, K.: Generating DNA code words using forbidding and enforcing systems. In: Dediu, A.-H., Martín-Vide, C., Truthe, B. (eds.) TPNC 2012. LNCS, vol. 7505, pp. 147–160. Springer, Heidelberg (2012)
Hopcroft, J.E., Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, Cambridge (1979)
Hussini, S., Kari, L., Konstantinidis, S.: Coding properties of DNA languages. Theor. Comput. Sci. 290, 1557–1579 (2003)
Jonoska, N., Kari, L., Mahalingam, K.: Involution solid and join codes. Fundamenta Informaticae 86, 127–142 (2008)
Jonoska, N., Mahalingam, K., Chen, J.: Involution codes: with application to DNA coded languages. Nat. Comput. 4, 141–162 (2005)
Jürgensen, H.: Syntactic monoids of codes. Acta Cybernetica 14, 117–133 (1999)
Jürgensen, H., Konstantinidis, S.: Codes. In: Rozenberg and Salomaa [26], pp. 511–607
Kari, L., Kitto, R., Thierrin, G.: Codes, involutions, and DNA encodings. In: Brauer, W., Ehrig, H., Karhumäki, J., Salomaa, A. (eds.) Formal and Natural Computing. LNCS, vol. 2300, pp. 376–393. Springer, Heidelberg (2002)
Kari, L., Konstantinidis, S., Kopecki, S.: Transducer descriptions of DNA code properties and undecidability of antimorphic problems (2015). arXiv preprint arXiv:1503.00035
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., Sosík, P.: Bond-free languages: formalizations, maximality and construction methods. IJFCS 16, 1039–1070 (2005)
Kari, L., Konstantinidis, S., Sosík, P.: On properties of bond-free DNA languages. Theor. Comput. Sci. 334, 131–159 (2005)
Kari, L., Sosík, P.: Aspects of shuffle and deletion on trajectories. Theor. Comput. Sci. 332, 47–61 (2005)
LaSer: Independent LAnguage SERver. http://laser.cs.smu.ca/independence/. Accessed February 2015
Mauri, G., Ferretti, C.: Word design for molecular computing: a survey. In: Chen, Junghuei, Reif, John H. (eds.) DNA 2003. LNCS, vol. 2943, pp. 37–47. Springer, Heidelberg (2004)
Rozenberg, G., Salomaa, A. (eds.): Handbook of Formal Languages, vol. I. Springer, Berlin (1997)
Shyr, H.: Free Monoids and Languages, 2nd edn. Hon Min Book Company, Taichung (1991)
Shyr, H., Thierrin, G.: Codes and binary relations. In: Malliavin, M.P. (ed.) Séminaire d’Algèbre Paul Dubreil, Paris 1975–1976 (29ème Année). Lecture Notes in Mathematics, vol. 586, pp. 180–188. Springer, Berlin (1977)
Stockmeyer, L., Meyer, A.: Word problems requiring exponential time (preliminary report). In: Proceedings of the 5th Annual ACM Symposium on Theory of Computing, pp. 1–9. ACM (1973)
Yu, S.: Regular languages. In: Rozenberg and Salomaa [26], pp. 41–110
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Kari, L., Konstantinidis, S., Kopecki, S. (2015). Transducer Descriptions of DNA Code Properties and Undecidability of Antimorphic Problems. In: Shallit, J., Okhotin, A. (eds) Descriptional Complexity of Formal Systems. DCFS 2015. Lecture Notes in Computer Science(), vol 9118. Springer, Cham. https://doi.org/10.1007/978-3-319-19225-3_12
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DOI: https://doi.org/10.1007/978-3-319-19225-3_12
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