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Abstract
We show that, from a topological point of view, 2-tape Buchi automata have the same accepting power than Turing machines equipped with a Buchi acceptance condition. In particular, for every non null recursive ordinal α, there exist some Σ$^{\rm 0}_{\alpha}$-complete and some Π$^{\rm 0}_{\alpha}$-complete infinitary rational relations accepted by 2-tape Buchi automata. This surprising result gives answers to questions of Simonnet [Sim92] and of Lescow and Thomas [Tho90, LT94].
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