Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Soundness of Unravelings for Conditional Term Rewriting Systems via
  Ultra-Properties Related to Linearity   Unravelings are transformations from a conditional term rewriting system
(CTRS, for short) over an original signature into an unconditional term
rewriting systems (TRS, for short) over an extended signature. They are not
sound w.r.t. reduction for every CTRS, while they are complete w.r.t.
reduction. Here, soundness w.r.t. reduction means that every reduction sequence
of the corresponding unraveled TRS, of which the initial and end terms are over
the original signature, can be simulated by the reduction of the original CTRS.
In this paper, we show that an optimized variant of Ohlebusch's unraveling for
a deterministic CTRS is sound w.r.t. reduction if the corresponding unraveled
TRS is left-linear or both right-linear and non-erasing. We also show that
soundness of the variant implies that of Ohlebusch's unraveling. Finally, we
show that soundness of Ohlebusch's unraveling is the weakest in soundness of
the other unravelings and a transformation, proposed by Serbanuta and Rosu, for
(normal) deterministic CTRSs, i.e., soundness of them respectively implies that
of Ohlebusch's unraveling.

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The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: q-alg
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The categories of this paper are: funct-an
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The categories of this paper are: supr-con
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The categories of this paper are: cmp-lg
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The categories of this paper are: mtrl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-th
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The categories of this paper are: math
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The categories of this paper are: dg-ga
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The categories of this paper are: stat
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The categories of this paper are: nlin