简而言之，DLS的提交规则是单链(One-Chain)的，允许节点仅由其自己的领导者提交。 PBFT、Tendermint和Casper中的提交规则几乎相同，由双链(Two-Chain)组成。 他们在介绍活动的机制上有所不同，PBFT具有二次方规模的leader“证明复杂度”（非线性），Tendermint和Casper在每个leader提议之前引入了强制性性的Δ延迟（非乐观响应性）。 HotStuﬀ使用三链(Three-Chain)规则，并具有无延迟的线性leader协议。
In this section, we examine four BFT replication protocols spanning four decades of research in Byzantine fault tolernace, casting them into a chained framework similar to Chained HotStuﬀ.
Figure 3 provides a birds-eye view of the commit rules of ﬁve protocols we consider, including HotStuﬀ.
In a nutshell, the commit rule in DLS  is One-Chain, allowing a node to be committed only by its own leader. The commit rules in PBFT , Tendermint [15, 16] and Casper  are almost identical, and consist of Two-Chains. They diﬀer in the mechanisms they introduce for liveness, PBFT has leader “proofs” of quadratic size (no Linearity), Tendermint and Casper introduce a mandatory ∆ delay before each leader proposal (no Optimistic Responsiveness). HotStuﬀ uses a Three-Chain rule, and has a linear leader protocol without delay.
The simplest commit rule is a One-Chain. Modeled after Dwork, Lynch, and Stockmeyer (DLS), the ﬁrst known asynchronous Byzantine Consensus solution, this rule is depicted in Figure 3(a). A replica becomes locked in DLS on the highest node it voted for.
Unfortunately, this rule would easily lead to a deadlock if at some height, a leader equivocates, and two correct replicas became locked on the conﬂicting proposals at that height. Relinquishing either lock is unsafe unless there are that indicate they did not vote for the locked value.
Indeed, in DLS only the leader of each height can itself reach a commit decision by the One-Chain commit rule. Thus, only the leader itself is harmed if it has equivocated. Replicas can relinquish a lock either if replicas did not vote for it, or if there are conﬂicting proposals (signed by the leader). The unlocking protocol occurring at the end of each height in DLS turns out to be fairly complex and expensive. Together with the fact that only the leader for a height can decide, in the best scenario where no fault occurs and the network is timely, DLS requires n leader rotations, and message transmissions, per single decision. While it broke new ground in demonstrating a safe asynchronous protocol, DLS was not designed as a practical solution.
Modeled after PBFT, a more practical appraoch uses a Two-Chain commit rule, see Figure 3(b). When a replica votes for a node that forms a One-Chain, it becomes locked on it. Conﬂicting One-Chains at the same height are simply not possible, as each has a QC, hence the deadlock situation of DLS is avoided.
However, if one replica holds a higher lock than others, a leader may not know about it even if it collects information from n − f replicas. This could prevent leaders from reaching decisions ad infinitum, purely due to scheduling. To get “unstuck”, the PBFT unlocks all replicas by carrying a proof consisting of the highest One-Chain’s by replicas. This proof is quite involved, as explained below.
The original PBFT, which has been open-sourced  and adopted in several follow up works [13, 34], a leader proof contains a set of messages collected from n − f replicas reporting the highest One-Chain each member voted for. Each One-Chain contains a QC, hence the total communication cost is . Harnessing signature combining methods from [45, 18], SBFT  reduces this cost to by turning each QC to a single value.
In the PBFT variant in , a leader proof contains the highest One-Chain the leader collected from the quorum only once. It also includes one signed value from each member of the quorum, proving that it did not vote for a higher One-Chain. Broadcasting this proof incurs communication complexity . Note that whereas the signatures on a QC may be combined into a single value, the proof as a whole cannot be reduced to constant size because messages from different members of the quorum may have different values.
In both variants, a correct replica unlocks even it has a higher One-Chain than the leader’s proof. Thus, a correct leader can force its proposal to be accepted during period of synchrony, and liveness is guaranteed. The cost is quadratic communication per leader replacement.
7.3 Tendermint 和 Casper
这个简单的领导者协议体现了HotStu ﬀ借鉴的领导者协议的通信复杂度的线性飞跃。如上所述，可以使用阈值签名将QC捕获为单个值，因此领导者可以收集和传播具有线性通信复杂性的最高单链。但是，至关重要的是，由于额外的QC步骤，HotStu ﬀ不需要领导者等待最大的网络延迟。
Tendermint has a Two-Chain commit rule identical to PBFT, and Casper has a Two-Chain rule in which the leaf does not need to have a QC to direct parent. That is, in Casper, Figure 3(c,d) depicts the commit rules for Tendermint and Casper, respectively.
In both methods, a leader simply sends the highest One-Chain it knows along with its proposal. A replica unlocks a One-Chain if it receives from the leader a higher one.
However, because correct replicas may not vote for a leader’s node, to guarantee progress a new leader must obtain the highest One-Chain by waiting the maximal network delay. Otherwise, if leaders only wait for the ﬁrst n − f messages to start a new height, there is no progress guarantee. Leader delays are inherent both in Tendermint and in Casper, in order to provide liveness.
This simple leader protocol embodies a linear leap in the communication complexity of the leader protocol, which HotStuﬀ borrows from. As already mentioned above, a QC could be captured in a single value using threshold signatures, hence a leader can collect and disseminate the highest One-Chain with linear communication complexity. However, crucially, due to the extra QC step, HotStuﬀ does not require the leader to wait the maximal network delay.