Local分布式决策
Local Distributed Decision
摘要：
分布式网络算法的一个中心主题是理解和处理局部性问题。受序贯复杂性理论的启发，本文重点研究了分布式决策问题的复杂性理论。在局部性的上下文中，解决决策问题需要处理器独立地检查它们的局部邻域，然后共同决定给定的全局输入实例是否属于某个指定的语言。本文介绍了几类分布式决策问题，证明了它们之间的分离性，并给出了一些完整的问题。更具体地说，我们认为标准的计算模型，并定义LD（本地决策）作为一类决策问题，可以解决在恒定数量的通信轮。我们首先研究随机化是否有助于本地分布式计算，以及在多大程度上的有趣的问题。具体来说，我们定义相应的随机化类BPLD，并询问LD是否=BPLD。我们提供了一个部分的答案，这个问题表明，在许多情况下，随机化并没有帮助决定遗传语言。此外，我们定义的概念，当地的多一个减少，并引入（不确定性）类NLD的决策问题，存在一个证书，可以验证在恒定数量的通信轮。我们证明了存在一个NLD-完全问题。我们还表明，存在的问题，而不是在全国民主联盟。另一方面，我们证明了类NLD#n，这是NLD假设每个处理器可以访问一个oracle，提供了网络中的节点数，包含所有（可判定）的语言。对于这类问题，我们也提供了一个自然的完全问题。
英文摘要：
A central theme in distributed network algorithms concerns understanding and coping with the issue of locality. Inspired by sequential complexity theory, we focus on a complexity theory for distributed decision problems. In the context of locality, solving a decision problem requires the processors to independently inspect their local neighborhoods and then collectively decide whether a given global input instance belongs to some specified language. This paper introduces several classes of distributed decision problems, proves separation among them and presents some complete problems. More specifically, we consider the standard LOCAL model of computation and define LD (for local decision) as the class of decision problems that can be solved in constant number of communication rounds. We first study the intriguing question of whether randomization helps in local distributed computing, and to what extent. Specifically, we define the corresponding randomized class BPLD, and ask whether LD=BPLD. We provide a partial answer to this question by showing that in many cases, randomization does not help for deciding hereditary languages. In addition, we define the notion of local many-one reductions, and introduce the (nondeterministic) class NLD of decision problems for which there exists a certificate that can be verified in constant number of communication rounds. We prove that there exists an NLD-complete problem. We also show that there exist problems not in NLD. On the other hand, we prove that the class NLD#n, which is NLD assuming that each processor can access an oracle that provides the number of nodes in the network, contains all (decidable) languages. For this class we provide a natural complete problem as well.
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。
