关于Brandt加速比定理从LOCAL到基于轮的全信息模型的推广
On Extending Brandt's Speedup Theorem from LOCAL to Round-Based Full-Information Models
摘要：
给定任何任务$Π$，勃兰特加速定理（PODC 2019）提供了一种机械的方法来设计另一个任务$Π'$，与$Π$相同的输入集，使得对于任何$t\geq 1$，$Π$在$t$轮中可解，当且仅当$Π'$在$t-1$轮中可解。该定理适用于匿名的变种，在图中有足够大的围长，并局部可检查标记（LCL）的任务。在本文中，使用组合拓扑应用于分布式计算，我们剖析了勃兰特的加速比定理的建设表示它在更广泛的框架轮为基础的模型支持全信息协议，其中包括不同的模型，如无等待共享内存计算迭代即时快照，同步无故障网络计算。特别是，我们提供的概念，如本地可查性和本地独立性的一般定义，在我们更广泛的框架。通过这种方式，我们能够确定计算模型和任务上的假设，这些假设足以应用勃兰特加速定理。更准确地说，我们确定哪些假设是充分的每个方向的if-and-only-if条件。有趣的是，这些假设是不同的性质。我们的一般方法能够将Brandt的加速比定理从有向网络扩展到有向网络、超图、动态网络，甚至扩展到包括过程之间的短循环依赖关系的图（即，大周长条件在某种程度上是不必要的）。该定理甚至可以扩展到共享内存的无等待计算。特别是，我们提供了新的不可能性证明的共识和完美的重命名2进程系统。
英文摘要：
Given any task $Π$, Brandt's speedup theorem (PODC 2019) provides a mechanical way to design another task~$Π'$ on the same input-set as $Π$ such that, for any $t\geq 1$, $Π$ is solvable in $t$ rounds if and only if $Π'$ is solvable in $t-1$ rounds. The theorem applies to the anonymous variant of the LOCAL model, in graphs with sufficiently large girth, and to locally checkable labeling (LCL) tasks. In this paper, using combinatorial topology applied to distributed computing, we dissect the construction in Brandt's speedup theorem for expressing it in the broader framework of round-based models supporting full information protocols, which includes models as different as wait-free shared-memory computing with iterated immediate snapshots, and synchronous failure-free network computing. In particular, we provide general definitions for notions such as local checkability and local independence, in our broader framework. In this way, we are able to identify the hypotheses on the computing model, and on the tasks, that are sufficient for Brandt's speedup theorem to apply. More precisely, we identify which hypotheses are sufficient for the each direction of the if-and-only-if condition. Interestingly, these hypotheses are of different natures. Our general approach enables to extend Brandt's speedup theorem from LOCAL to directed networks, to hypergraphs, to dynamic networks, and even to graphs including short cyclic dependencies between processes (i.e., the large girth condition is, to some extend, not necessary). The theorem can even be extended to shared-memory wait-free computing. In particular, we provide new impossibility proofs for consensus and perfect renaming in 2-process systems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
