可检测目标空间复杂度的上下界
Upper and Lower Bounds on the Space Complexity of Detectable Object
摘要：
具有非易失性主存储器（NVM）的系统的出现增加了对对崩溃故障鲁棒的\emph{recoverable concurrent objects}的设计的兴趣，因为它们的操作能够通过使用NVM中保留的状态从这样的故障中恢复。特别感兴趣的是可恢复算法，除了确保对象的一致性，还提供了\emph{detectability}，一个正确性条件，要求恢复代码可以推断失败的操作是否被线性化，并在前一种情况下，获得其响应。在这项工作中，我们调查的可检测算法的空间复杂度和外部支持，他们需要。我们作出以下三项贡献。首先，我们提出了第一个无等待的有界空间可检测的读/写和CAS对象实现。其次，我们证明了每个$N$过程的无障碍可检测CAS实现的位复杂度，假设值来自大小至少为$N$的域，是$Ω(N)$。最后，我们证明了以下适用于大型对象类的无障碍可检测实现：它们的可恢复操作必须提供\emph{auxiliary state} --不可恢复的对应实现不需要的状态--其值必须从操作外部提供，无论是由系统还是由操作的调用者提供。相反，如果可恢复算法不可检测，则通常不需要这种外部支持。
英文摘要：
The emergence of systems with non-volatile main memory (NVM) increases the interest in the design of \emph{recoverable concurrent objects} that are robust to crash-failures, since their operations are able to recover from such failures by using state retained in NVM. Of particular interest are recoverable algorithms that, in addition to ensuring object consistency, also provide \emph{detectability}, a correctness condition requiring that the recovery code can infer if the failed operation was linearized or not and, in the former case, obtain its response. In this work, we investigate the space complexity of detectable algorithms and the external support they require. We make the following three contributions. First, we present the first wait-free bounded-space detectable read/write and CAS object implementations. Second, we prove that the bit complexity of every $N$-process obstruction-free detectable CAS implementation, assuming values from a domain of size at least $N$, is $Ω(N)$. Finally, we prove that the following holds for obstruction-free detectable implementations of a large class of objects: their recoverable operations must be provided with \emph{auxiliary state} -- state that is not required by the non-recoverable counterpart implementation -- whose value must be provided from outside the operation, either by the system or by the caller of the operation. In contrast, this external support is, in general, not required if the recoverable algorithm is not detectable.
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