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The minimum execution requirement of task τ i, denoted as P i, is defined as the time that τ i takes to execute when it is assigned to an infinite number of cores6, i.e., (P_{i} = sum _{k=1}^{n_{i}} c_{s_{i}^{k}}), where (c_{s_{i}^{k}}) denotes the worst-case execution time among the sub-tasks of segment k.
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