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Found such categorization from "mLSM: Making Authenticated Storage Faster in Ethereum" paper https://www.usenix.org/system/files/conference/hotstorage18/hotstorage18-paper-raju.pdf.

There are different types of nodes in an ethereum network - fullNode, fastNode and lightNode. A fullNode downloads the entire history of blockchain from the beginning while a lightNode downloads only the block headers and gets the block bodies on demand from a fullNode through RPC calls. Ethereum runs ETH protocol between two fullNode in the cluster, and LES protocol to manage the interaction between a lightNode and a fullNode in the cluster. A fullNode returns a merkle proof along with the requested data to a lightNode. A merkle proof is simply the list of hash values in the tree on the path from the requested value node to the root node. A lightNode can verify if the data is cryptographically correct or not using the merkle proof.

To be honest, I have not heard such classification in the past 2-3 years. Which leads me to question the relevance of the paper and such node categorization.

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Originally the classification was due to the method used to synchronize. Later it changed to the functionality provided. Full nodes were archival nodes, they keep the whole story of the transaction execution. Fast nodes are regular nodes that only maintain the history of most recent blocks. Light nodes are the same, they keep a minimal amount of data and use other nodes when more data is needed.

There are several factors that made running a node not feasible. The increased costs of storage and bandwidth, L2 networks becoming more popular, and the switch to proof of stake broke light protocol.

There is ongoing research to use verkle trees to improve storage. Until those changes are implemented running a node will be difficult for individuals.

The classification is adequate but not very useful in practice.

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