Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Forward and Backward Application of Symbolic Tree Transducers   We consider symbolic tree automata (sta) and symbolic tree transducers (stt).
We characterize s-recognizable tree languages (which are the tree languages
recognizable by sta) in terms of (classical) recognizable tree languages and
relabelings. We prove that sta and the recently introduced variable tree
automata are incomparable with respect to their recognition power. We define
symbolic regular tree grammars and characterize s-regular tree languages in
terms of regular tree languages and relabelings. As a consequence, we obtain
that s-recognizable tree languages are the same as s-regular tree languages.
  We show that the syntactic composition of two stt computes the composition of
the tree transformations computed by each stt, provided that (1) the first one
is deterministic or the second one is linear and (2) the first one is total or
the second is nondeleting. We consider forward application and backward
application of stt and prove that the backward application of an stt to any
s-recognizable tree language yields an s-recognizable tree language. We give a
linear stt of which the range is not an s-recognizable tree language. We show
that the forward application of simple and linear stt preserves
s-recognizability. As a corollary, we obtain that the type checking problem of
simple and linear stt and the inverse type checking problem of arbitrary stt is
decidable.

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The categories of this paper are: gr-qc
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The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: chao-dyn
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The categories of this paper are: math-ph
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The categories of this paper are: q-alg
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The categories of this paper are: adap-org
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-lat
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The categories of this paper are: funct-an
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The categories of this paper are: eess
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The categories of this paper are: quant-ph