Multiprocessor real-time operating systems such as VxWorks, LynxOS, QNX, and real-time variants of Linux allow each task to have an arbitrary processor affinity (APA), which is the set of processors on which the task is allowed to execute. Gujarati et al. (2013, 2015a) developed two schedulability analyses for hard real-time tasks subject to such APA constraints: a reduction-based approach, first presented at ECRTS 2013 (Gujarati et al. 2013), and an approach based on linear programming (LP), which was introduced in this journal (Gujarati et al. 2015a) alongside a discussion of the earlier reduction-based technique. Unfortunately, the reduction-based technique was later found to be partially flawed (Gujarati et al. 2015b). This letter serves to document the flaw (alongwith illustrative counterexamples) and to correct the reduction-based approach presented by Gujarati et al. (2015a). To avoid further errors, the corrected claims have been formally verified with Prosa (Cerqueira et al. 2016a, b), a recently developed framework for mechanized schedulability anal-

中文翻译：

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通讯文章：修正基于约简的APA调度的可调度性分析

多处理器实时操作系统（例如 VxWorks、LynxOS、QNX 和 Linux 的实时变体）允许每个任务具有任意处理器关联 (APA)，这是允许任务在其上执行的处理器集。古吉拉特语等。(2013, 2015a) 为受此类 APA 约束的硬实时任务开发了两种可调度性分析：一种基于缩减的方法，首次在 ECRTS 2013 上提出（Gujarati 等人，2013 年），以及一种基于线性规划 (LP) 的方法，这是在本期刊（Gujarati et al. 2015a）中介绍的，同时讨论了早期的基于减少的技术。不幸的是，后来发现基于减少的技术存在部分缺陷（Gujarati et al. 2015b）。这封信用于记录缺陷（以及说明性的反例）并纠正 Gujarati 等人提出的基于减少的方法。(2015a)。为避免进一步的错误，更正后的声明已通过 Prosa（Cerqueira 等人，2016a，b）正式验证，这是一个最近开发的机械化可调度分析框架。