These talks are based on joint work with Elizabeth Goode (Delaware; Ph.D. Binghamton 1999).
I will start with a quick introduction to splicing theory for the uninitiated. The emphasis will be on Head's original question, asking for a characterization of splicing languages among regular languages. Here splicing languages are defined in terms of a finite initial language under the iterated application of finitely many splicing rules. I shall give a number of examples of such splicing languages.
Although an abstract splicing language may not be reflexive, those that model biochemical phenomena in the classical manner are necessarily reflexive (and also symmetric). Our main result relates to the subclass of reflexive splicing languages: We provide an algorithm which determines whether a regular language is in this subclass. It appears that our methods also give a recognition algorithm for the subclass of reflexive and symmetric splicing languages. Unfortunately, we have examples to show that our methods (at this time) do not provide an algorithm to determine whether a regular language is a splicing language, so this question remains open.