Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Transforming Narrowing Trees into Regular Tree Grammars Generating
  Ranges of Substitutions   The grammar representation of a narrowing tree for a syntactically
deterministic conditional term rewriting system and a pair of terms is a
regular tree grammar that generates expressions for substitutions obtained by
all possible innermost-narrowing derivations that start with the pair and end
with particular non-narrowable terms. In this paper, under a certain syntactic
condition, we show a transformation of the grammar representation of a
narrowing tree into another regular tree grammar that overapproximately
generates the ranges of ground substitutions generated by the grammar
representation. In our previous work, such a transformation is restricted to
the ranges w.r.t. a given single variable, and thus, the usefulness is limited.
We extend the previous transformation by representing the range of a ground
substitution as a tuple of terms, which is obtained by the coding for finite
trees. We show a precise definition of the transformation and prove that the
language of the transformed regular tree grammar is an overapproximation of the
ranges of ground substitutions generated by the grammar representation. We
leave an experiment to evaluate the usefulness of the transformation as future
work.

3
The categories of this paper are: physics
2
The categories of this paper are: math
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn