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Ethereum: Does the Bitcoin Blockchain Solve the Byzantine General Problem?
The Byzantine General Problem (BGP) is a complex computational puzzle first proposed by Dimitris J. Christodoulou and Silvio Micali in 1980. It is a challenging problem for Byzantine networks (BNets). Ethereum. BGP states: given a number of nodes in a graph, determine whether at most two nodes can agree on any given value.
Bitcoin Blockchain and the Byzantine General Problem
While the Bitcoin blockchain solves some problems related to Byzantine Generals, such as the difficulty of solving a linear congruence equation (a form of BGP), the Ethereum mainnet blockchain does not solve the problem directly. However, it provides an alternative approach that can be used in conjunction with other solutions.
Bitcoin Blockchain Solution
A Bitcoin block is essentially a set of transactions that have been bundled together and verified by a network of miners. These nodes work together to confirm the transactions and create a new block. One way to think of this process as resolving BGP is through the concept of “consensus.”
In the context of blockchain, consensus refers to an agreement between nodes on the collective state of the network. For example, when multiple nodes in a graph agree on a value (e.g., a timestamp), it means that all nodes have reached a consensus. This consensus process is not directly related to resolving BGP, but rather serves as a mechanism to ensure that nodes maintain a common view of the state of the blockchain.
Ethereum’s Approach
Ethereum, built on top of the proof-of-work (PoW) consensus algorithm, offers an alternative approach to resolving BGP. One way to solve the problem is to use “distributed subscriptions,” which involve combining multiple sources of information into a single, authoritative subscription.
In Ethereum, nodes can participate in the network and contribute their local subscription information (e.g., transaction timestamps) to gain a common view of the state of the blockchain. This allows nodes to agree on the collective state of the network without relying solely on central authorities or consensus mechanisms like Bitcoin.
Example: Ethereum’s Byzantine General Problem Solving
To illustrate how Ethereum solves BGP, consider the following scenario:
Imagine two nodes, node A and node B, connected in a graph. Each node has its own local subscription information (e.g., transaction timestamps) for a given block of transactions. The goal is to determine whether it is possible for at most two nodes to agree on the collective state of the network.
Node A knows that node B has verified all the transactions in this block and is therefore “valid”. However, node B does not necessarily know anything about other blocks or transactions outside of its local subscription information. In this case, node A can use Ethereum’s distributed mechanisms to combine multiple sources of information (e.g., node timestamps) and produce a single, authoritative subscription.
This allows node A to determine whether at most two nodes agree on the collective state of the network, which solves the Byzantine General Problem for that block. This approach provides an alternative solution to the BGP problem that is more robust against Byzantine attacks.
Conclusion
In summary, while the Bitcoin blockchain solves some of the problems associated with the Byzantine General Problem, the Ethereum mainnet blockchain does not directly solve the problem. However, Ethereum’s distributed subscription method can be used in conjunction with other solutions to provide an alternative method for solving the BGP problem.
