Dennis Pixton and Elizabeth Goode
Recognizing splicing languages: syntactic monoids and simultaneous pumping (dvi, pdf, postscript)
in Discrete Applied Math., 155 (2007), 989-1006.

We use syntactic monoid methods, together with an enhanced pumping lemma, to investigate the structure of splicing languages. We obtain an algorithm for deciding whether a regular language is a reflexive splicing language, but the general question remains open.