feat(avm-pil-backend): public input columns

[dbanks12]

Overview

As mentioned in the hackmd below, public inputs to the avm will be performed in a very similar way to how halo2 injects public inputs through their advice columns.

A dedicated column will contain public inputs that can be reconstructed by the verifier.

Approach

Annotate a special column with the public attribute, create an example proving system ( toy avm ) that will test the construction of these

Likely Obstacles

It is not clear whether barretenberg already has a way to construct public inputs in this way ( where the verifier is required to compute a commitment to a column ). If it does not have this functionality, then it will need to be implemented

[dbanks12]

https://hackmd.io/8kkJo4RkRTG6mpwL8fOf3w