Define block kernel inputs/outputs

[Fumuran]

What should be done?

Define the kernel inputs and outputs for the block of transactions.

How should it be done?

To be clarified

When is this task done?

To be clarified

Additional context

No response

[bobbinth]

We can arrange block kernel inputs in a similar manner to batch kernel inputs described in https://github.com/0xPolygonMiden/miden-base/issues/919#issuecomment-2423408808, though block kernel inputs could be a bit simpler:

Inputs:  [BATCHES_COMMITMENT]
Outputs: [BLOCK_HASH, NULLIFIER_COMMITMENT]

Where

• BATCHES_COMMITMENT is a sequential hash of batch_ids (a batch ID is assumed to be sequential hash of (transaction_id, account_id) tuples for transaction that went into the batch).
• BLOCK_HASH is the hash of the block header for the newly created block.
• NULLIFIER_COMMITMENT is the commitment to the set of nullifiers created in the block.

We don't output account update commitment separately because I think this can be computed from the data underlying the BATCHES_COMMITMENT. But if that becomes difficult, we can certainly add something like ACCOUNT_UPDATES_COMMITMENT to the outputs.