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A blockchain is a replicated state machine at its core. A state machine is a computer science concept, in which a machine can have multiple states but only one state at a time. It follows a state transition process (or a set of defined processes), which is the only way the state changes from the old or initial state (S) to a new state (S').
The state transition function in a blockchain is synonymous with a transaction. Given an initial state, a confirmed transaction, and a set of rules for interpreting that transaction, the machine transitions to a new state. The rules of interpretation are defined at the application layer.