We introduce the theoretical foundations of the Tangle 2.0, a probabilistic leaderless consensus protocol based on a directed acyclic graph (DAG) called the Tangle. The Tangle naturally succeeds the blockchain as its next evolutionary step as it offers features suited to establish more efficient and scalable distributed ledger solutions. Consensus is no longer found in the longest chain but on the heaviest DAG, where PoW is replaced by a stake- or reputation-based weight function. The DAG structure and the underlying Reality-based UTXO Ledger allow parallel validation of transactions without the need for total ordering. Moreover, it enables the removal of the intermediary of miners and validators, allowing a pure two-step process that follows the \emph{propose-vote} paradigm at the node level and not at the validator level. We propose a framework to analyse liveness and safety under different communication and adversary models. This allows providing impossibility results in some edge cases and in the asynchronous communication model. We provide formal proof of the security of the protocol assuming a common random coin.

翻译：我们引入了Tangle 2.0的理论基础,这是一个基于定向环形图(DAG)的概率性无领导者共识协议,称为Tangle。Tangle自然继承了块链的下一个进化步骤,因为它提供了适合建立更有效和可缩放的分类账解决方案的特征。共识不再出现在最长的链条上,而是出现在最重的DAG上,PoW被一个基于利益或声誉的权重功能所取代。DAG结构和基于Reality的UTXO Ledger基础允许对交易进行平行的验证,而无需完全订购。此外,它允许清除矿工和验证员的中间人,允许在节级而不是在验证层面上遵循\emph{propostion-vote}范式的纯粹的两步进程。我们提出了一个框架,用于分析不同通信和敌机模式下的生活和安全性。这样可以在某些边缘案件和不连贯的通信模式下提供不可能的结果。我们正式证明协议的安全性,假设一个共同随机的硬币。