Abstract In DNA splicing system, DNA molecules are cut and recombined with the presence of restriction enzymes and a ligase. The splicing system is analyzed via formal language theory where the molecules resulting from the splicing system generate a language which is called a splicing language. In nature, DNA molecules can be read in two ways; forward and backward. A sequence of string that reads the same forward and backward is known as a palindrome. Palindromic and non-palindromic sequences can also be recognized in restriction enzymes. Research on splicing languages from DNA splicing systems with palindromic and non-palindromic restriction enzymes have been done previously. This research is motivated by the problem of DNA assembly to read millions of long DNA sequences where the concepts of automata and grammars are applied in DNA splicing systems to simplify the assembly in short-read sequences. The splicing languages generated from DNA splicing systems with palindromic and non- palindromic restriction enzymes are deduced from the grammars which are visualised as automata diagrams, and presented by transition graphs where transition labels represent the language of DNA molecules resulting from the respective DNA splicing systems.