On the weight of universal insertion grammars

We study the computational power of pure insertion grammars. We show that pure insertion grammars of weight 3 can characterize all recursively enumerable languages. This is achieved by either applying an inverse morphism and a weak coding, or a left (right) quotient with a regular language. We also study an application in DNA computing and improve some known results concerning the power of insertion-deletion DNA systems.

[1]  Grzegorz Rozenberg,et al.  Handbook of Formal Languages , 1997, Springer Berlin Heidelberg.

[2]  Lila Kari,et al.  Contextual Insertions/Deletions and Computability , 1996, Inf. Comput..

[3]  Kamala Krithivasan,et al.  On Characterizing Recursively Enumerable Languages by Insertion Grammars , 2005, Fundam. Informaticae.

[4]  Gheorghe Paun,et al.  Context-free insertion-deletion systems , 2005, Theor. Comput. Sci..

[5]  Rani Siromoney,et al.  Circular contextual insertions/deletions with applications to biomolecular computation , 1999, 6th International Symposium on String Processing and Information Retrieval. 5th International Workshop on Groupware (Cat. No.PR00268).

[6]  Solomon Marcus,et al.  Contextual Grammars , 1969, COLING.

[7]  Carlos Martín-Vide,et al.  Characterizations of Recursively Enumerable Languages by Means of Insertion Grammars , 1998, Theor. Comput. Sci..

[8]  István Katsányi.  A Note on Restricted Insertion-Deletion Systems , 2004, Bull. EATCS.

[9]  Gheorghe Paun,et al.  Representations and Characterizations of Languages in Chomsky Hierarchy by Means of Insertion-Deletion Systems , 2008, Int. J. Found. Comput. Sci..

[10]  Gheorghe Paun,et al.  DNA Computing: New Computing Paradigms , 1998 .

[11]  榊原 康文,et al.  G. Paun, G. Rozenberg and A. Salomaa : "DNA Computing-New Computing Paradigms", Springer-Verlag (1998) , 2000 .

[12]  Takashi Yokomori,et al.  On the computational power of insertion-deletion systems , 2004, Natural Computing.