Relative strength of the XOR Hypothesis versus the k-SUM Hypothesis

Ascertain whether the XOR Hypothesis is stronger than, weaker than, or equivalent to the k-SUM Hypothesis.

Background

The paper considers both the integer k-SUM and the vector-parity k-XOR problems, noting that both admit meet-in-the-middle algorithms with similar runtimes and have analogous hardness hypotheses.

While the paper derives implications from either hypothesis to the Primal Treewidth SETH, it highlights that the precise relationship between the two hypotheses is not settled.