Year: 2025
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Hughes, Jared A., Helton, J. William
Language: English
Subfield: Computer Networks and Communications
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4415026618
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