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$I$ is a set of instances;

given an instance $x\; in\; I$, $f(x)$ is the set of feasible solutions;

given an instance $x$ and a feasible solution $y$ of $x$, $m(x,\; y)$ denotes the measure of $y$, which is usually a positive real.

$g$ is the goal function, and is either $min$ or $max$.

$I$ can be recognized in polynomial time, and

the size of a feasible solution is polynomially bounded by the instance size.