We show that reachability, repeated reachability, nontermination and unboundedness are NP-complete for Lossy Channel Machines that are flat, i.e., with no nested cycles in the control graph. The upper complexity bound relies on a fine analysis of iterations of lossy channel actions and uses compressed word techniques for efficiently reasoning with paths of exponential lengths. The lower bounds already apply to acyclic or single-path machines.

中文翻译：

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在平坦有损信道机器上

我们表明，对于平坦的有损通道机器，即控制图中没有嵌套循环，可达性、重复可达性、非终止性和无界性是 NP 完全的。复杂度上限依赖于对有损通道动作迭代的精细分析，并使用压缩字技术对指数长度的路径进行有效推理。下限已经适用于非循环或单路径机器。