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arXiv · 2505.01628

The Satisfiability Threshold for K-XOR Games

Jared A. Hughes·J. William Helton
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Abstract

A $K$-XORGAME system corresponds to a $K$-XORSAT system with the additional restriction that the variables divide uniformly into $K$ blocks. This forms a system of $m$ equations with $K n$ unknowns over $\mathbb{Z}_2$, and a perfect strategy corresponds to a solution to these equations. Equivalently, such equations correspond to colorings of a $K$-uniform $K$-partite hypergraph. This paper proves that the satisfiability threshold of $m/n$ for $K$-XORGAME problems exists and equals the satisfiability threshold for $K$-XORSAT.

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BibTeXRIS

Jared A. Hughes, J. William Helton. 2025-05-02. The Satisfiability Threshold for K-XOR Games. https://arxiv.org/abs/2505.01628

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