Top-down Transducers Research Articles

Balancedness of MSO transductions in polynomial time

We show that MSO definable tree-to-string transductions with a fixed copy number, given as top-down tree-to-string transducers with fixed copying-bound, can be checked for balancedness of all output strings in polynomial time. We also present an upper bound for the copying bound for deterministic top-down transducers and show that in general, balancedness of output languages of deterministic finite-copying top-down tree-to-string transducers is DExptime-hard.

On the equivalence problem for letter-to-letter top-down tree transducers

Letter to letter top-down tree transducers are investigated in this paper. Informally, trees which appear in the rules of such transducers are reduced to one letter in the right-hand side as in the left one. With an encoding of the tree transformations induced by such transducers into recognizable forests, we recently established the decidability of equivalence for linear top-down transducers. Here, in order to capture the non-linearity of top-down transducers, we introduce new classes of tree automata with equivalence constraints between direct subterms for which equivalence is decidable. We then show that the equivalence problem for non-linear top-down transducers can be reduced to the equivalence problem of automata with equivalence constraints.

The Copying Power of One-State Tree Transducers

One-state deterministic top-down transducers (or tree homomorphisms) cannot handle ''prime copying'', i.e. their class of output (string) languages is not closed under the operation L ( -> { (w)^f(n) | w in L, f(n) >= 1 } ) , where f is any integer function whose range contains numbers with arbitrary large prime factors (such as a polynomial). The exact amount of nonclosure under these copying operations is established for several classes of input (tree) languages. These results are relevant to the extended definable (or restricted parallel level) languages, to the syntax-directed translation of context-free languages and to the tree transducer hierarchy.