New variants of insertion and deletion systems in formal languages

Abstract

In formal language theory, the operations of insertion and deletion are generalizations of the operations of concatenation and left/right quotients. The insertion operation interpolates one word in an arbitrary place within the other while the deletion operation extracts the word from an arbitrary position of another word. Previously, insertion and deletion have been applied to model the recombinance of DNA and RNA molecules in DNA computing, where contexts were used to mimic the site of enzymatic activity. However, in this research, new systems are introduced by taking motivation from the atomic behaviour of chemical compounds during chemical bonding, in which the concept of a balanced arrangement is required for a successful bonding. Besides that, the relation between insertion and deletion systems and group theory are also shown. Here, insertion and deletion systems are constructed with bonds and also interactions; hence new variants of insertion and deletion systems are introduced. The first is bonded systems, which are introduced by defining systems with restrictions that work on the bonding alphabet. The other variant is systems with interactions, which are introduced by utilizing the binary operations of certain groups as the systems’ interactions. From this research, the generative power and closure properties of the newly introduced bonded systems are determined, and a language hierarchy is constructed. In addition, group generating insertion systems are introduced and illustrated using Cayley graphs. Therefore, this research introduced new variants of insertion and deletion systems that contribute to the advancement of DNA computing and also showcased their application in group theory.