Bonded sequential and parallel insertion-deletion systems in formal language theory

Abstract

Insertion and deletion are set operations that act upon structures in a predetermined fashion to create language generating devices in formal language theory, a field that involves the mathematical aspects of logic and set theory. Earlier, insertion and deletion systems that simulate the process of chemical bonding between atoms had been introduced, called bonded insertion and deletion systems. Still, these bonded systems could not generate up to recursively enumerable languages, nor could they generate abstract families of languages. Thus, the aim of this research is to introduce bonded insertion-deletion systems by combining the two aforementioned systems. Additionally, the generative power and closure properties of the sequential and parallel variants of bonded insertion-deletion systems are determined by simulating computationally complete grammars and by direct proofs, respectively. From there, graphs are constructed to visualize the mechanism of the new bonded systems by using concepts in graph theory. Furthermore, a new cryptosystem that involves both encoding and encryption is constructed using bonded sequential and parallel insertiondeletion systems based on an American Standard Code for Information Interchange (ASCII) table framework involving a bonding alphabet. From this research, it has been shown that the generative power of the new systems is up to the family of recursively enumerable languages, hence capable of generating abstract families of languages. The graphs of bonded systems and language generating graphs have been constructed such that the language of the graphs is equivalent to the language of the systems. On the other hand, the newly constructed cryptosystem using bonded insertion-deletion systems is able to confidentially store or transfer information. The findings in this research are important to advance studies in the field of DNA computing by effectively increasing the generative power of previous bonded systems, visualizing the mechanism of derivations of bonded systems, as well as providing an alternative method for information security with a nexus of bio-inspired cryptosystems.