Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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.

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The categories of this paper are: math
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: eess
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The categories of this paper are: q-bio
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The categories of this paper are: cond-mat
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The categories of this paper are: physics
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The categories of this paper are: nlin
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The categories of this paper are: stat
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The categories of this paper are: solv-int
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The categories of this paper are: quant-ph
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The categories of this paper are: econ