This work considers exact schedulability analysis of a set of aperiodic non-preemptive tasks on a given set of computational resources, and the problem is known to be NP-Complete. We propose four different SAT-based encoding schemes to address the exact schedulability problem. Each approach requires a different number of variables and generates a distinct number of clauses. We present extensive comparative studies on those approaches for both theoretical and practical results. Interestingly, the encoding scheme that requires the least number of variables is one of the worst encoding schemes among the four. We observe that it is not only the number of variables but also the other factors such as the number of clauses, the number of literals per clause, etc. dictate the performance. Moreover, the solver can play significant role on the performance. Hence, an efficient encoding scheme is absolutely necessary to find a solution quickly for resource-constrained systems.

这项工作考虑了在给定的一组计算资源上对一组非周期性非抢先任务的精确可调度性分析，并且已知该问题是NP-Complete。我们提出了四种不同的基于SAT的编码方案来解决确切的可调度性问题。每种方法都需要使用不同数量的变量，并生成不同数量的子句。我们针对这些方法的理论和实践结果进行了广泛的比较研究。有趣的是，需要最少数量的变量的编码方案是这四种中最差的编码方案之一。我们观察到，不仅是变量的数量，而且其他因素（例如，子句的数量，每个子句的文字数量等）也决定了性能。而且，求解器可以对性能起重要作用。