The properties of semi-simple splicing system over alternating group, A₃

Splicing system was introduced by Head in 1987 in order to explore the recombinant behaviour of deoxyribonucleic acid (DNA) strands in the presence of restriction enzymes and ligases. Restriction enzymes cut the DNA strands into a left - pattern and right-pattern while the ligases recombine the left-pattern of the first string with the right-pattern of the second string and vice-versa. Semi-simple splicing system is a variant of splicing system where the splicing of DNA strands will be at two distinct sites. Splicing languages generated from the splicing system are classified based on their computational power, according to the Chomsky Hierarchy. Previous researchers found that the splicing system of finite set of strings and rules generates only regular languages which has the lowest computational power. Hence, some restriction has been introduced to increase the computational power of splicing languages generated. In this research, an element of alternating group of order three is associated with the initial strings of semi-simple splicing system to generate non-regular languages which has higher computational power. Some lemmas and theorems are proven to show that associating the alternating group to the initial strings could increase the computational power of the splicing languages.