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Hardness Results for Static Priority Real-Time Scheduling
<span title="">2012</span>
<i title="IEEE">
<a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2zm4ggc525ejnjqnwf3k4zbp74" style="color: black;">2012 24th Euromicro Conference on Real-Time Systems</a>
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Real-time systems are often modeled as a collection of tasks, describing the structure of the processor's workload. In the literature, task-models of different expressiveness have been developed, ranging from the traditional periodic task model to highly expressive graph-based models. For dynamic priority schedulers, it has been shown that the schedulability problem can be solved efficiently, even for graphbased models. However, the situation is less clear for the case of static priority
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<a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/ecrts.2012.13">doi:10.1109/ecrts.2012.13</a>
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... ers. It has been believed that the problem can be solved in pseudo-polynomial time for the generalized multiframe model (GMF). The GMF model constitutes a compromise in expressiveness by allowing cycling through a static list of behaviors, but disallowing branching. Further, the problem complexity for more expressive models has been unknown so far. In this paper, we show that previous results claiming that a precise and efficient test exists are wrong, giving a counterexample. We prove that the schedulability problem for GMF models (and thus also all more expressive models) using static priority schedulers is in fact coNP-hard in the strong sense. Our result thus establishes the fundamental hardness of analyzing static priority real-time scheduling, in contrast to its dynamic priority counterpart of pseudo-polynomial complexity.
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