# Research on Progress of Blockchain Consensus Algorithm:
## 3 Blockchain Consensus Algorithm
### Consensus Algorithm Concept  
In 1959, [PERSON] and [PERSON] carried out a subjective probability consensus study: that is, how many individuals with subjective consciousness in the same space can reach a consistent consensus probability distribution under certain conditions. In fact, this is the early consistency problem, and in some cases, it is also called the consensus problem, and this article uniformly expresses it as the consistency problem. **Definition 1**. : _(Consistency problem[47; 48]): It refers to a series of operations performed by multiple nodes in blockchain network, and it is difficult for the data results obtained and saved by each node to reach consistency to a certain extent._  
The early consistency problem only focused on scenarios where the number of nodes was limited and trustworthy, but such scenarios had greater limitations and were not suitable for open Internet scenarios. The scholar [PERSON] extended the consistency problem to the Internet environment with open scenes and massive nodes in the Bitcoin system he designed, and he proposed a distributed consensus mechanism that considers the possibility of malicious nodes in the environment, that is, a consensus algorithm that focuses on the Byzantine Generals problem, which has trans-era significance and scientific research value. **Definition 2**. : _(Byzantine failures[49]): It refers to the problem of how to reach a cooperative consensus among various nodes distributed in the network environment, with possible malicious nodes. In the blockchain, Byzantine error is a concrete manifestation of the Byzantine Generals problem. It refers to the fact that independent components in a blockchain network can do arbitrary or malicious behaviors, and these components may cooperate with other faulty components, thereby affecting the correct results of node calculations in the blockchain._ \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Feature** & **Type** & **Public Chain** & **Consortium Chain** & **Private Chain** \\ \hline
**Participant** & Any node &
\begin{tabular}{c} Consortium \\ members only \\ \end{tabular} & Individual or company \\ \hline
**Accounter** & All participating nodes &
\begin{tabular}{c} Determined by \\ negotiation among \\ consortium members \\ \end{tabular} & Determined within the \\ \hline
**Degree of centralization** & Decentralized &
\begin{tabular}{c} Polycentric \\ \end{tabular} & Polycentric \\ \hline
**Advantage** & Tamper-proof, reliable & High efficiency, low cost & High efficiency, low cost \\ \hline
**Application scenario** & Digital currency & Payment, transaction & Audit, issue \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of the blockchain characteristics based on three different models. The consensus algorithm is a means to ensure the data consistency of each node for a certain proposal. However, there are always differences in the computing power, storage, and other machine configurations of each node in a blockchain. Different consensus algorithms and consensus mechanisms have different capabilities to ensure that nodes obtain balanced accounting rights. If some nodes always easily obtain the right to accounting, it will undoubtedly cause other nodes to lose the activity to participate in the competition for accounting, thus making the entire blockchain network inactive. **Definition 3**. : _(**Activeness**): It refers to the proportion of nodes in blockchain network that actively participate in the competition for accounting rights of the data block, block information verification, as well as other work per unit time.