1 research outputs found
An Algebraic Model For Quorum Systems
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.Comment: 15 pages, 3 algorithm