Support arithmetic evaluation chiplet (ACE) in AirScript

[Al-Kindi-0]

What should be done?

Once the ACE chiplet added to the VM, we should add support for it in AirScript.

How should it be done?

When we can go from constraints written in AirScript to arithmetic circuits compatible with the finalized design of the ACE chiplet.

When is this task done?

When the arithmetic evaluation chiplet is part of the VM.

Additional context

The discussion in 0xPolygonMiden/miden-vm#1610

[bobbinth]

I think the task here is mainly adding a new backend for AirScript. This backend would lower the algebraic graph into an arithmetic circuit where each gate is represented by a field element in the following format: op | input_wire_1_id | input_wire_2_id | output_wire_id. op defines an operation to be performed on input wires which could be either add or mul (and maybe sub).

We do have an open question about what's the best way to handle wire initialization and also constant values. One approach is to do it via input operation.