Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Polynomial-time kernel reductions   In the framework of computational complexity and in an effort to define a
more natural reduction for problems of equivalence, we investigate the recently
introduced kernel reduction, a reduction that operates on each element of a
pair independently. This paper details the limitations and uses of kernel
reductions. We show that kernel reductions are weaker than many-one reductions
and provide conditions under which complete problems exist. Ultimately, the
number and size of equivalence classes can dictate the existence of a kernel
reduction. We leave unsolved the unconditional existence of a complete problem
under polynomial-time kernel reductions for the standard complexity classes.

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The categories of this paper are: hep-th
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The categories of this paper are: adap-org
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The categories of this paper are: physics
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The categories of this paper are: hep-ph
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The categories of this paper are: q-bio
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The categories of this paper are: math-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: patt-sol
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The categories of this paper are: supr-con
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The categories of this paper are: stat
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The categories of this paper are: q-alg
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The categories of this paper are: astro-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: math
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The categories of this paper are: bayes-an
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The categories of this paper are: plasm-ph