Quorum系统的一个代数模型
An Algebraic Model For Quorum Systems
摘要：
仲裁系统是分布式容错计算中用于捕获信任假设的关键数学抽象。quorum系统是所有进程的子集的集合，称为quorums，具有每对quorums具有非空交集的属性。它们可以在许多可靠的分布式系统的核心中找到，例如云计算平台，分布式存储系统和区块链。在本文中，我们给出了一个新的解释的法定人数系统，从经典的多数为基础的法定人数系统，并将其扩展到拜占庭法定人数系统。我们提出了一个代数表示的理论基础的法定人数系统利用多元多项式理想，将这些系统的属性，并研究其代数品种。为了实现这个目标，我们将利用布尔Groebner基地的性质。布尔Groebner基的良好性质使我们能够避免检查quorum系统的一致性和可用性所需的部分组合计算。我们的研究结果提供了一种新的方法来测试从代数和算法的角度来看，仲裁系统的属性。
英文摘要：
Quorum systems are a key mathematical abstraction in distributed fault-tolerant computing for capturing trust assumptions. A quorum system is a collection of subsets of all processes, called quorums, with the property that each pair of quorums have a non-empty intersection. They can be found at the core of many reliable distributed systems, such as cloud computing platforms, distributed storage systems and blockchains. In this paper we give a new interpretation of quorum systems, starting with classical majority-based quorum systems and extending this to Byzantine quorum systems. We propose an algebraic representation of the theory underlying quorum systems making use of multivariate polynomial ideals, incorporating properties of these systems, and studying their algebraic varieties. To achieve this goal we will exploit properties of Boolean Groebner bases. The nice nature of Boolean Groebner bases allows us to avoid part of the combinatorial computations required to check consistency and availability of quorum systems. Our results provide a novel approach to test quorum systems properties from both algebraic and algorithmic perspectives.
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