In an earlier question we've discussed what kind of program the Merovingian is and it's widely agreed that he's an operating system to an earlier version of the matrix - a predecessor to the Oracle.
Persephone, however, is his long suffering companion and lover. They have apparently been together for some time.
Persephone: A long time ago, when we first came here, it was so different.
Do we have any information on what sort of program she was? From the scene in the bathroom with Neo my guess is that she's something to do with human emotion, maybe even love... but I'm extremely curious if anyone else has worked out anything else.