Contextual Insertions/Deletions and Computability

We investigate two generalizations of insertion and deletion of words, that have recently become of interest in the context of molecular computing. Given a pair of words (x, y), called a context, the (x, y)-contextual insertion of a word v into a word u is performed as follows. For each occurrence of xy as a subword in u, we include in the result of the contextual insertion the words obtained by inserting v into u, between x and y. The (x, y)contextual deletion operation is defined in a similar way. We study closure properties of the Chomsky families under the defined operations, contextual ins-closed and del-closed languages, and decidability of existence of solutions to equations involving these operations. Moreover, we prove that every Turing machine can be simulated by a system based entirely on contextual insertions and deletions. ] 1996 Academic Press