Iterating Inverse Binary Transducers

Iterating Invertible Binary Transducers

We study iterated transductions defined by a class of invertible transducers over the binary alphabet. The transduction semigroups of these automata turn out to be free Abelian groups and the orbits of finite words can be described as affine subspaces in a suitable geometry defined by the generators of these groups. We show that iterated transductions are rational for a subclass of our automata.

Macro forest transducers

Xml documents conceptually are not trees, but forests. Therefore, we extend the concept of macro tree transducers (mtt’s) to a transformation formalism of forests, macro forest transducers (mft’s). We show that mft’s form a strict superset of mtt’s operating on forests (represented as binary trees). On the other hand, the transformation of every mft can be simulated by the composition of two mt...

XML Type Checking for Macro Tree Transducers with Holes

Macro forest transducers (mfts) extend macro tree transducers (mtts) from ranked to unranked trees. Mfts are more powerful than mtts (operating on binary tree encodings) because they support sequence concatenation of output trees as build-in operation. Surprisingly, inverse type inference for mfts, for a fixed output type, can be done within the same complexity as for mtts. Inverse type inferen...

Iterating Transducers

Languages in AC de ned by iterating nite transducers

We present an explicit construction of AC circuits that simulate nite state transducer iteration. Our approach yields circuits with only Θ(n log(n)) linear fan-in gates, whereas the circuits built from standard proof of L ⊆ AC use matrix multiplication and hence have Θ(n log(n)) such gates.