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QP versus NP

Frank Vega

Given an instance of $\textit{XOR 2SAT}$ with $m$ clauses and a positive integer $K$ given in unary, the problem majority exclusive-or 2-satisfiability consists in deciding whether this Boolean formula has a truth assignment with at leat $K$ satisfiable clauses and $K \geq \frac{2}{3} \times m$. Majority exclusive-or 2-satisfiability is in $QP$ and $NP-complete$. Thus, $QP \subseteq NP$.

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