The robust construction of the ledger data structure is an essential ingredient for the safe operation of a distributed ledger. While in traditional linear blockchain systems, permission to append to the structure is leader-based, in Directed Acyclic Graph-based ledgers, the writing access can be organised leaderless. However, this leaderless approach relies on fair treatment of non-referenced blocks, i.e. tips, by honest block issuers. We study the impact of a deviation from the standard tip selection by a subset of block issuers with the aim of halting the confirmation of honest blocks entirely. We provide models on this so-called orphanage of blocks and validate these through open-sourced simulation studies. A critical threshold for the adversary issuance rate is shown to exist, above which the tip pool becomes unstable, while for values below the orphanage decrease exponentially. We study the robustness of the protocol with an expiration time on tips, also called garbage collection, and modification of the parent references per block.

翻译：账本数据结构的稳健构建是分布式账本安全运行的关键要素。在传统线性区块链系统中，对数据结构的追加权限采用基于领导者（leader-based）的机制，而在基于有向无环图（DAG）的账本中，写入访问权可通过无领导者（leaderless）方式组织。然而，这种无领导者方法依赖于诚实区块发行者对未引用区块（即"tricks"）的公平处理。我们研究了部分区块发行者偏离标准"tip选择"策略所产生的影响——其目的是完全阻止诚实区块的确认。针对这种所谓的区块"孤子化"现象，我们建立了数学模型，并通过开源仿真研究进行了验证。研究发现，存在一个关键的攻击者发行速率阈值：当该速率超过阈值时，tips池将变得不稳定；而低于该阈值时，孤子化程度呈指数级衰减。我们还研究了设置tips过期时间（即垃圾回收机制）以及修改每个区块的父引用（parent references）对协议鲁棒性的影响。