分布式计算弱异步模型的决策能力
Decision Power of Weak Asynchronous Models of Distributed Computing
摘要：
Esparza和Reiter最近对分布式计算的模型进行了系统的比较研究，分布式计算由相同的有限状态自动机组成的网络组成，这些有限状态自动机合作决定网络的底层图是否满足给定的属性。该研究根据四个标准对模型进行分类，并表明20种最初可能的组合根据其决策能力（即每个类别的自动机可以决定的属性）分解为7个等价类。然而，Esparza和Reiter只显示了类之间的（适当的）包含，因此没有证明它们的决策能力。在本文中，我们这样做的标签属性，即属性只依赖于节点的标签，但不依赖于图的结构。特别地，多数（携带标签$a$的节点是否多于携带标签$b$的节点）是标记属性。我们的研究结果表明，只有一个由Esparza和Reiter确定的7个等价类可以决定任意网络的多数。然后，我们研究了有界度网络上的类的表达能力，并表明三个类可以。特别是，我们提出了一个算法的大多数，适用于所有有界度网络下的对抗调度器，即即使调度器必须满足每个节点的移动无限频繁，并证明没有这样的算法可以工作的任意网络。
英文摘要：
Esparza and Reiter have recently conducted a systematic comparative study of models of distributed computing consisting of a network of identical finite-state automata that cooperate to decide if the underlying graph of the network satisfies a given property. The study classifies models according to four criteria, and shows that twenty initially possible combinations collapse into seven equivalence classes with respect to their decision power, i.e. the properties that the automata of each class can decide. However, Esparza and Reiter only show (proper) inclusions between the classes, and so do not characterise their decision power. In this paper we do so for labelling properties, i.e. properties that depend only on the labels of the nodes, but not on the structure of the graph. In particular, majority (whether more nodes carry label $a$ than $b$) is a labelling property. Our results show that only one of the seven equivalence classes identified by Esparza and Reiter can decide majority for arbitrary networks. We then study the expressive power of the classes on bounded-degree networks, and show that three classes can. In particular, we present an algorithm for majority that works for all bounded-degree networks under adversarial schedulers, i.e. even if the scheduler must only satisfy that every node makes a move infinitely often, and prove that no such algorithm can work for arbitrary networks.
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。
