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for questions involving inequalities, upper and lower bounds.

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Complexity of Deciding Feasibility of a system of linear inequalities over restricted variables

If you do this out, you will get a system of linear inequalities as follows: $$ a_{11}x_0+\cdots+a_{1m}x_{m-1} \geq 0\\\ \vdots \\\ a_{n1}x_0+\cdots+a_{nm}x_{m-1} \geq 0 $$ Question: What is the time … complexity of only deciding whether this system of linear inequalities is feasible, meaning there exists some $\vec{x}\in\left\lbrace 1, -1\right\rbrace^m$ that satisfies the constraints. …
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