On the Accepting Power of 2-Tape Büchi Automata

We show that, from a topological point of view, 2-tape Büchi automata have the same accepting power than Turing machines equipped with a Büchi acceptance condition. In particular, for every non null recursive ordinal α, there exist some Σ α -complete and some Π α -complete infinitary rational relations accepted by 2-tape Büchi automata. This surprising result gives answers to questions of Simonnet [Sim92] and of Lescow and Thomas [Tho90,LT94].