The structure of reflexive regular splicing languages via Schützenberger constants

The splicing operation was introduced in 1987 by Head as a mathematical model of the recombination of DNA molecules under the influence of restriction and ligases enzymes. This operation allows us to define a computing (language generating) device, called a splicing system. Other variants of this original definition were also proposed by Paun and Pixton respectively. The computational power of splicing systems has been thoroughly investigated. Nevertheless, an interesting problem is still open, namely the characterization of the class of regular languages generated by finite splicing systems. In this paper, we will solve the problem for a special class of finite splicing systems, termed reflexive splicing systems, according to each of the definitions of splicing given by Paun and Pixton. This special class of systems contains, in perticular, finite Head splicing systems. The notion of a constant, given by Schützenberger, once again intervenes.