Both ways rational functions

Abstract

We consider binary relations on words which can be recognized by finite two-tape devices in two different ways: the traditional way where the two tapes are scanned in the same direction and a new one where they are scanned in different directions. The devices of the former type define the family of rational relations, while those of the latter define an a priori really different family. We characterize the partial functions that are in the intersection of the two families. We state a conjecture for the intersection for general, nonfunctional, relations.