Deterministic top-down tree transducers with iterated look-ahead

Abstract

It is known that by iterating the look-ahead tree languages for deterministic top-down tree automata, more and more powerful recognizing devices are obtained. Let DR 0 = DR, where DR is the class of all tree languages recognizable by deterministic top-down tree automata, and let, for n ⩾ 1, DR n be the class of all tree languages recognizable by deterministic top-down tree automata with DR n−1 look-ahead. Then DR 0 ⊂ DR 1 ⊂ DR 2 ⊂…. Slutzki and Vágvölgyi (1993) showed that the composition powers of the class of all deterministic top-down tree transformations with deterministic top-down look-ahead ( DTT DR ) form a proper hierarchy, i.e. ( DTT DR ) n ⊂( DTT DR ) n + 1 for n ⩾ 0. Along the proof they studied the notion of the deterministic top-down tree transducer with DR n look-ahead (dtt DR n ) and showed that ( DTT DR ) n + 1 ⊆ DTT DR n ( n ⩾ 0), where DTT DR n stands for the class of all tree transformations induced by dtt DR n 'S. Our aim is to show the reversed inclusion, i.e. DTT DR n ⊆ ( DTT DR ) n + 1 ( n ⩾ 0). This implies a precise characterization DTT DR n = ( DTT DR ) n + 1 ( n ⩾ 0), and implies that the classes DTT DR n ( n⩾ 0) form a proper hierarchy.