Abstract
Matrix insertion-deletion systems are a class of insertion-deletion systems, where insertion and deletion rules are grouped in sequences, and it is known that such systems with two symbols context-free insertion and deletion rules are not computationally complete. In this work, matrix insertion-deletion systems with exo-operations (MIDEs, in short) are proposed, where insertion and deletion operations are applied only at the ends of a string (called exo-operations). The computation power of context-free MIDEs as language generators is investigated. We prove that context-free MIDEs of matrices size two with one symbol insertion and two symbols deletion are computationally complete, and so are systems with two symbols insertion and one symbol deletion. Moreover, if the size of matrices is three, the computational completeness can also be reached by context-free MIDEs with one symbol insertion and one symbol deletion. These results show that the computational power of MIDEs is strictly increased by introducing the exo-operations of insertion and deletion.
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References
Alhazov, A., Krassovitskiy, A., Rogozhin, Y., Verlan, S.: P systems with insertion and deletion exo-operations. Fund. Inform. 110(1–4), 13–28 (2011)
Alhazov, A., Krassovitskiy, A., Rogozhin, Y.: Circular post machines and P systems with exo-insertion and deletion. In: Gheorghe, M., Păun, G., Rozenberg, G., Salomaa, A., Verlan, S. (eds.) LNCS, vol. 7184, pp. 73–86. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-28024-5_7
Benne, R.: RNA Editing: The Alteration of Protein Coding Sequences of RNA. Ellis Horwood, Chichester (1993)
Biegler, F., Burrell, M.J., Daley, M.: Regulated RNA rewriting: modelling RNA editing with guided insertion. Theor. Comput. Sci. 387(2), 103–112 (2007)
Castellanos, J., MartÃn-Vide, C., Mitrana, V., Sempere, J.M.: Networks of evolutionary processors. Acta Inform. 39(6–7), 517–529 (2003)
Daley, M., Kari, L., Gloor, G., Siromoney, R.: Circular contextual insertions/deletions with applications to biomolecular computation. In: Proceeding of the String Processing and Information Retrieval Symposium & International Workshop on Groupware, pp. 47–54 (1999)
Freund, R., Kogler, M., Rogozhin, Y., Verlan, S.: Graph-controlled insertion-deletion systems. In: McQuillan, I., Pighizzini, G. (eds.) Proceeding of 12th Workshop on Descriptional Complexity of Formal Systems, vol. 31, pp. 88–98 (2010)
Haussler, D.: Insertion and iterated insertion as operations on formal languages. Ph.D. thesis, University of Colorado at Boulder (1982)
Kari, L.: On insertion and deletion in formal languages. Ph.D. thesis, University of Turku (1991)
Kari, L., Păun, Gh., Thierrin, G., Yu, S.: At the crossroads of DNA computing and formal languages: characterizing RE using insertion-deletion systems. In: Proceeding of 3rd DIMACS Workshop on DNA Based Computing, Philadelphia, pp. 318–333 (1997)
Krassovitskiy, A., Rogozhin, Y., Verlan, S.: Computational power of insertion-deletion (P) systems with rules of size two. Nat. Comput. 10(2), 835–852 (2011)
Kudlek, M., Rogozhin, Y.: Small universal circular post machines. Comput. Sci. J. Moldova 9(1), 34–52 (2001)
Marcus, S.: Contextual grammars. Rev. Roum. Math. Pures Appliquées 14, 1525–1534 (1969)
Margenstern, M., Păun, G., Rogozhin, Y., Verlan, S.: Context-free insertion-deletion systems. Theor. Comput. Sci. 330(2), 339–348 (2005)
Păun, G.: Marcus Contextual Grammars. Kluwer Academic Publishers, Norwell (1997)
Rozenberg, G., Salomaa, A.: DNA computing: new ideas and paradigms. In: Wiedermann, J., van Emde Boas, P., Nielsen, M. (eds.) ICALP 1999. LNCS, vol. 1644, pp. 106–118. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-48523-6_9
Păun, G.: Membrane Computing: An Introduction. Springer, Heidelberg (2002). https://doi.org/10.1007/978-3-642-56196-2
Peng, H., Wang, J., Pérez-Jiménez, M.J., Riscos-Núñez, A.: An unsupervised learning algorithm for membrane computing. Inf. Sci. 304, 80–91 (2015)
Petre, I., Verlan, S.: Matrix insertion-deletion systems. Theor. Comput. Sci. 456, 80–88 (2012)
Rozenberg, G., Salomaa, A. (eds.): Handbook of Formal Languages: Volume 3 Beyond Words. Springer, Berlin (1997). https://doi.org/10.1007/978-3-642-59126-6
Song, B., Song, T., Pan, L.: A time-free uniform solution to subset sum problem by tissue P systems with cell division. Math. Struct. Comp. Sci. 27(1), 17–32 (2017)
Song, B., Zhang, C., Pan, L.: Tissue-like P systems with evolutional symport/antiport rules. Inf. Sci. 378, 177–193 (2017)
Verlan, S.: On minimal context-free insertion-deletion systems. J. Autom. Lang. Comb. 12(1–2), 317–328 (2007)
Verlan, S.: Recent developments on insertion-deletion systems. Comput. Sci. J. Moldova 18(2), 210–245 (2010)
Zhang, G., Gheorghe, M., Pan, L., Pérez-Jiménez, M.J.: Evolutionary membrane computing: a comprehensive survey and new results. Inf. Sci. 279, 528–551 (2014)
Acknowledgements
The work was supported by National Key R&D Program of China for International S&T Cooperation Projects (No. 2017YFE0103900), National Natural Science Foundation of China (61320106005, 61425002, 61502186, 61602192, and 61772214), and China Postdoctoral Science Foundation (2016M600592, 2016M592335, and 2017T100554).
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Song, B., Xu, F., Pan, L. (2018). On Languages Generated by Context-Free Matrix Insertion-Deletion Systems with Exo-Operations. In: Graciani, C., Riscos-Núñez, A., Păun, G., Rozenberg, G., Salomaa, A. (eds) Enjoying Natural Computing. Lecture Notes in Computer Science(), vol 11270. Springer, Cham. https://doi.org/10.1007/978-3-030-00265-7_22
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