Context-free insertion-deletion systems

  • Authors:
  • Maurice Margenstern;Gheorghe Paun;Yurii Rogozhin;Sergey Verlan

  • Affiliations:
  • Université de Metz, LITA, UFR MIM Ile du Saulcy, 57045 Metz Cedex, France;Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, 70700 Bucureşti, Romania and Department of Computer Science and Al, University of Sevilla, Avda. Reina Mercedes s/n, 41012 Se ...;Institute of Mathematics and Computer Science, Academy of Sciences of Moldova, Str. Academiei 5, 2028, Chişinau, Moldova;Université de Metz, LITA, UFR MIM Ile du Saulcy, 57045 Metz Cedex, France

  • Venue:
  • Theoretical Computer Science - Descriptional complexity of formal systems
  • Year:
  • 2005

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Abstract

We consider a class of insertion-deletion systems which have not been investigated so far, those without any context controlling the insertion-deletion operations. Rather unexpectedly, we found that context-free insertion-deletion systems characterize the recursively enumerable languages. Moreover, this assertion is valid for systems with only one axiom, and also using inserted and deleted strings of a small length. As direct consequences of the main result we found that set-conditional insertion-deletion systems with two axioms generate any recursively enumerable language (this solves an open problem), as well as that membrane systems with one membrane having context-free insertion-deleletion rules without conditional use of them generate all recursively enumerable languages (this improves an earlier result). Some open problems are also formulated.