3,914 research outputs found
Storage-to-tree transducers with look-ahead
AbstractWe generalize Engelfriet's decomposition result stating that the class of transformations induced by top–down tree transducers with regular look-ahead is equal to the composition of the class of top–down tree transformations and the class of linear tree homomorphisms. Replacing the input trees with an arbitrary storage type, the top–down tree transducers are turned into regular storage-to-tree transducers. We show that the class of transformations induced by regular storage-to-tree transducers with positive look-ahead is equal to the composition of the class of transformations induced by regular storage-to-tree transducers with the class of linear tree homomorphisms. We also show that the classes of transformations induced by both IO and OI context-free storage-to-tree transducers are closed under positive look-ahead, and are closed under composition with linear tree homomorphisms
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
Top-down tree transducers with two-way tree walking look-ahead
AbstractWe consider top-down tree transducers with deterministic, nondeterministic and universal two-way tree walking look-ahead and compare the transformational powers of their deterministic and strongly deterministic versions by giving the inclusion diagram of the induced tree transformation classes. We also study the closure properties of these transformation classes with respect to composition
Deciding Linear Height and Linear Size-to-Height Increase for Macro Tree Transducers
In this paper we study Macro Tree Transducers (MTT), specifically the Linear
Height Increase ("LHI") and Linear input Size to output Height ("LSHI")
constraints. In order to decide whether a Macro tree transducer (MTT) is of LHI
or LSHI, we define a notion of depth-properness: a MTT is depth-proper if, for
each state, there is no bound to the depth at which it places its argument
trees. We show how to effectively put a MTT in depth-proper form. For MTTs in
Depth-proper form, we characterize the LSH property as equivalent to the
finite-nesting property, and we characterize the LHI property as equivalent to
the finiteness of a new type of nesting which we call Multi-Leaf-nesting (or
ML-nesting). As opposed to regular nesting where we look at the nesting of
states applied to a single input node, we count the nesting of states applied
to nodes that are not ancestors of each other. We use this characterization to
give a decision procedure for the LSHI and LHI properties. Finally we consider
the decision problem of the LSOI (Linear input Size to number of distinct
Output subtrees Increase) property. A long standing open problem is whether MTT
of LSOI are as expressive as Attribute Tree Transducers (ATT), in this paper we
show that deciding whether a MTT is of LSOI is as hard as deciding the
equivalence of ATTs
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