\begin{definition}[Linear Constraints]
    Let $V$ be a fixed set of integer Variables $\{x_1, x_2, \dots, n\} $. A linear constraint is defined as $\psi = a_0 + a_1 x_1 + \dots + a_n x_n \diamond 0$ where $a_i \in \mathbb{N}$ are integer coefficients, $x_i \in V$ are variables and $\diamond \in \{>, <, \geq, \leq, =\}$.
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