Semi-simple splicing systems

In 1987 Tom Head [5] introduced the idea of splicing as a generative mechanism in formal language theory. This mechanism was popularized and extensively developed by Gheorghe Păun and his many coworkers, who recognized much of the subtlety and power of this mechanism and who used it as a foundation for the rapidly developing study of DNA based computing. See, for example, [11] and [12]. (The most necessary definitions are reviewed briefly in section 2.) However, one of Head’s most basic questions is still unanswered. It was established early that a finite splicing system would always produce a regular splicing language ([1], [13]), but not all regular languages can be generated in this way (a simple example is (aa)∗). Thus there remains the problem of precisely characterizing such splicing languages. One of the first papers by Păun and his coworkers was [9], which introduced the notion of a simple splicing system. It is our goal here to give a simple description of the languages that result from a generalization of this notion, which we call a semi-simple splicing system. We are not interested in generalizing the results of [9], although our methods give simpler approaches even in the simple splicing case. Rather, we are interested in illustrating some approaches towards characterizing splicing languages in general. Our main result is a characterization of semi-simple splicing languages in terms of certain directed graphs; this is carried out in sec∗Research partially supported by DARPA/NSF CCR-9725021.