On the computational power of insertion-deletion systems

Gene insertion and deletion are basic phenomena found in DNA processing or RNA editing in molecular biology. The genetic mechanism and development based on these evolutionary transformations have been formulated as a formal system with two operations of insertion and deletion, called insertion-deletion systems (Kari and Thierrin, 1996; Kari et al., 1997). We investigate the generative power of insertion-deletion systems (InsDel systems), and show that the family INS ¹ ₁ DEL ¹ ₁ is equal to the family of recursively enumerable languages. This gives a positive answer to an open problem posed in Kari et al. (1997) where it was conjectured contrary.