Deciding Equivalence of Linear Tree-to-Word Transducers in Polynomial Time

We show that the equivalence of deterministic linear top-down tree-to-word transducers is decidable in polynomial time. Linear tree-to-word transducers are non-copying but not necessarily order-preserving and can be used to express XML and other document transformations. The result is based on a partial normal form that provides a basic characterization of the languages produced by linear tree-to-word transducers.Comment: short version of this paper will be published in the proceedings of the 20th Conference on Developments in Language Theory (DLT 2016), Montreal, Canad

Tree transducers, L systems, and two-way machines

A relationship between parallel rewriting systems and two-way machines is investigated. Restrictions on the “copying power” of these devices endow them with rich structuring and give insight into the issues of determinism, parallelism, and copying. Among the parallel rewriting systems considered are the top-down tree transducer; the generalized syntax-directed translation scheme and the ETOL system, and among the two-way machines are the tree-walking automaton, the two-way finite-state transducer, and (generalizations of) the one-way checking stack automaton. The. relationship of these devices to macro grammars is also considered. An effort is made .to provide a systematic survey of a number of existing results

The copying power of one-state tree transducers

One-state deterministic top-down tree 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 ε L, f(n) ≥ 1}, where f is any integer function whose range contains numbers with arbitrarily 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.\ud \u

Multiple Context-Free Tree Grammars: Lexicalization and Characterization

Multiple (simple) context-free tree grammars are investigated, where "simple" means "linear and nondeleting". Every multiple context-free tree grammar that is finitely ambiguous can be lexicalized; i.e., it can be transformed into an equivalent one (generating the same tree language) in which each rule of the grammar contains a lexical symbol. Due to this transformation, the rank of the nonterminals increases at most by 1, and the multiplicity (or fan-out) of the grammar increases at most by the maximal rank of the lexical symbols; in particular, the multiplicity does not increase when all lexical symbols have rank 0. Multiple context-free tree grammars have the same tree generating power as multi-component tree adjoining grammars (provided the latter can use a root-marker). Moreover, every multi-component tree adjoining grammar that is finitely ambiguous can be lexicalized. Multiple context-free tree grammars have the same string generating power as multiple context-free (string) grammars and polynomial time parsing algorithms. A tree language can be generated by a multiple context-free tree grammar if and only if it is the image of a regular tree language under a deterministic finite-copying macro tree transducer. Multiple context-free tree grammars can be used as a synchronous translation device.Comment: 78 pages, 13 figure

The Equivalence Problem for Deterministic MSO Tree Transducers is Decidable

It is decidable for deterministic MSO definable graph-to-string or graph-to-tree transducers whether they are equivalent on a context-free set of graphs

Three hierarchies of transducers

Composition of top-down tree transducers yields a proper hierarchy of transductions and of output languages. The same is true for ETOL systems (viewed as transducers) and for two-way generalized sequential machines