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Splicing system and sofic shift

Splicing systems are mathematical models that are used for sets of DNA sequences generated through repeated chemical reactions of DNA sequences, which were introduced by Head in 1987 [4]. Although a splicing system specifies a regular language, it is known that all regular languages cannot be generated by a splicing system. Symbolic dynamical systems are sets of infinite sequences that are closely related to formal languages. In this manuscript, several characterizations of the splicing system are given using the theory of symbolic dynamical systems.