2,508 research outputs found
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
Linear Bounded Composition of Tree-Walking Tree Transducers: Linear Size Increase and Complexity
Compositions of tree-walking tree transducers form a hierarchy with respect
to the number of transducers in the composition. As main technical result it is
proved that any such composition can be realized as a linear bounded
composition, which means that the sizes of the intermediate results can be
chosen to be at most linear in the size of the output tree. This has
consequences for the expressiveness and complexity of the translations in the
hierarchy. First, if the computed translation is a function of linear size
increase, i.e., the size of the output tree is at most linear in the size of
the input tree, then it can be realized by just one, deterministic,
tree-walking tree transducer. For compositions of deterministic transducers it
is decidable whether or not the translation is of linear size increase. Second,
every composition of deterministic transducers can be computed in deterministic
linear time on a RAM and in deterministic linear space on a Turing machine,
measured in the sum of the sizes of the input and output tree. Similarly, every
composition of nondeterministic transducers can be computed in simultaneous
polynomial time and linear space on a nondeterministic Turing machine. Their
output tree languages are deterministic context-sensitive, i.e., can be
recognized in deterministic linear space on a Turing machine. The membership
problem for compositions of nondeterministic translations is nondeterministic
polynomial time and deterministic linear space. The membership problem for the
composition of a nondeterministic and a deterministic tree-walking tree
translation (for a nondeterministic IO macro tree translation) is log-space
reducible to a context-free language, whereas the membership problem for the
composition of a deterministic and a nondeterministic tree-walking tree
translation (for a nondeterministic OI macro tree translation) is possibly
NP-complete
Streaming Tree Transducers
Theory of tree transducers provides a foundation for understanding
expressiveness and complexity of analysis problems for specification languages
for transforming hierarchically structured data such as XML documents. We
introduce streaming tree transducers as an analyzable, executable, and
expressive model for transforming unranked ordered trees in a single pass.
Given a linear encoding of the input tree, the transducer makes a single
left-to-right pass through the input, and computes the output in linear time
using a finite-state control, a visibly pushdown stack, and a finite number of
variables that store output chunks that can be combined using the operations of
string-concatenation and tree-insertion. We prove that the expressiveness of
the model coincides with transductions definable using monadic second-order
logic (MSO). Existing models of tree transducers either cannot implement all
MSO-definable transformations, or require regular look ahead that prohibits
single-pass implementation. We show a variety of analysis problems such as
type-checking and checking functional equivalence are solvable for our model.Comment: 40 page
Bottom-up and top-down tree transformations - a comparison
The top-down and bottom-up tree transducer are incomparable with respect to their transformation power. The difference between them is mainly caused by the different order in which they use the facilities of copying and nondeterminism. One can however define certain simple tree transformations, independent of the top-down/bottom-up distinction, such that each tree transformation, top-down or bottom-up, can be decomposed into a number of these simple transformations. This decomposition result is used to give simple proofs of composition results concerning bottom-up tree transformations.\ud
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A new tree transformation model is introduced which generalizes both the top-down and the bottom-up tree transducer
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