Note, the concept of "valid" is application dependent, as defined by the customer's business logic. The transition rules, as defined by the Exchange itself, are unknown to the application's smart contract. The smart contract is aware only of a succinct commitment to the state. Any specific state transition is dependent on the executed transactions (which are not transmitted on-chain to enhance scalability).
C_1if there is knowledge of:
C_0is its commitment.
C_1is its commitment.
t_0, t_1, ..., t_kexecutable (one after the other) on
S_0(implying valid state transitions – as defined by the application rules), such that the resulting state is