Deterministic Top-Down Tree Transducers with Iterated Lookahead

It is known that by iterating the look-ahead tree languages for deterministic topdown tree automata, more and more powerful recognizing devices are obtained. Let DR0 = DR, where DR is the class of all tree languages recognizable by deterministic top-down tree automata, and let, for n 1, DRn be the class of all tree languages recognizable by deterministic top-down tree automata with DRn 1 lookahead. Then DR0 DR1 DR2 : : : . Slutzki and V agvolgyi [17] showed that the composition powers of the class of all deterministic top-down tree transformations with deterministic top-down look-ahead (DTT) form a proper hierarchy i.e. (DTT) (DTTDR)n+1 for n 0. Along the proof they studied the notion of the deterministic top-down tree transducer with DRn look-ahead (dtt n) and showed that (DTTDR)n+1 DTTn (n 0), where DTTn stands for the class of all tree transformations induced by dttn 's. Our aim is to show the reversed inclusion, i.e. DTTn (DTTDR)n+1 (n 0). This implies a precise characterization DTTn = (DTTDR)n+1 (n 0), and implies that the classes DTTn (n 0) form a proper hierarchy.