A Modified Merkle Patricia Trie is a specialized cryptographic data structure used by Ethereum to store and verify its state. It merges the tamper-evident hashing of a Merkle tree (where every value can be verified against a single root hash) with the efficient key-based lookup and insertion of a radix (Patricia) trie, enabling secure, verifiable storage of accounts, balances, and smart contract data.

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The Ethereum state refers to the current status of all accounts, balances, smart contract codes, and storage on the Ethereum blockchain. It is represented as a large, cryptographic data structure known as a Modified Merkle Patricia Trie. This state is updated dynamically each time a new block of transactions is processed by the network.

Ethereum State

A Merkle Tree, or binary hash tree, is a data structure used to encode blockchain data more efficiently and securely. In bitcoin's blockchain​, transactions are run through an algorithm to generate hashes, which are then concatenated together to form one hash for the entire block. The resulting tree allows users to verify a specific transaction without downloading the whole blockchain.

Merkle Tree

Modified Merkle Patricia Trie

The Ethereum State Transition Function, formally denoted as $$Y(S, TX) \rightarrow S'$$, defines how the Ethereum blockchain moves from a current state $$S$$ to a new state $$S'$$ after executing a transaction $$TX$$. It is the core mechanism for processing and validating state changes.

Ethereum State Transition Function

In Ethereum, the state is made up of objects called "accounts", with each account having a 20-byte address and state transitions being direct transfers of value and information between accounts. An Ethereum account contains four fields:

-The nonce, a counter used to make sure each transaction can only be processed once
-The account's current ether balance
-The account's contract code, if present
-The account's storage 

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