BTC State Transition Function

Based on the system architecture described above, we can readily deduce the state transition function for the Bitcoin finite state machine model like below.

1. Let the initial state of a user address A be represented as Si=State(A), where State() is a query function that returns the transaction history associated with that user.

2. A conditional transaction initiated by user A can be abstracted as a state transition function Ti= UTXO_OP().

3. The verification of computational integrity is represented as Vi = Verify(Si+1, Si, Ti).

Therefore, the complete global state transition function for A can be abstracted as:

Si x Ti x V → Si+1