One application of a keyed-verification credential system, anonymous or otherwise, is secure client-side encoding of a state machine. Rather than having a server maintain state for each client in a central database, a server can offload state to its clients, relying on the security of the credential to prevent clients from tampering with their state.
This is particularly interesting when the credential system is an anonymous credential system, because clients can prove statements about their (previously-authenticated) state in zero knowledge, rather than revealing the state itself.
However, usefully encoding a state machine requires creating credentials that can only be presented once. Borrowing terminology from substructural type systems, these could be called "affine credentials".
Extending CMZ13 credentials to have use-once semantics is easy, by adding a nullifier attribute to a credential. During issuance, clients generate a random nullifier and requests blinded issuance of a credential with that nullifier. During presentation, clients reveal the nullifier, allowing the issuer to perform a set membership query.
This approach gives a hard guarantee that credentials are not presented twice, at the cost of requiring the issuer to maintain a nullifier set. However, the nullifier set can be continually pruned using the epoch system described in the next section.