Polynomial-time kernel reductions

Jeffrey Finkelstein; Benjamin Hescott

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arXiv · 1604.08558

Polynomial-time kernel reductions

Jeffrey Finkelstein·Benjamin Hescott

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Abstract

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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Jeffrey Finkelstein, Benjamin Hescott. 2016-04-28. Polynomial-time kernel reductions. https://arxiv.org/abs/1604.08558

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