The SL2 languages are speci?ed with a set of 2-factors in Σ2 (plus some factors in {?}Σ and some factors in Σ{?} distinguishing symbols that may occur at the beginning and end of the string, respectively), the recognizable languages are speci?ed with triples in Q × Q × Σ (along with an indication of the start and accepting states). In studying the SL languages, it was useful to consider those factors as tiles, allowing us to generate strings in the language recognized by the SL-automaton by laying them out in overlapping sequences. We can develop a similar generator model from our FSAs by extending the triples of the edge relation with triples from {?}×Q×{?} (to designate starting tiles)