Constraint register read/write about olavm HOT 2 CLOSED

After some thinking, we should not read data from register in the generate_trace phase. generate_trace is only used to re-format trace into stark way. So the proper way would be: We keep 16 register columns, we do read/write in constraint phase.

from olavm.

For register's consistency, we treat all columns as a set of row. Also refer from winterfell. From zk point of view, it just handles numbers, here, register(and memory also) is just a set of numbers.

So here comes question: do we need a register consistency constraint, just like a memory consistency constraint? For all register columns, constraints their initial state, transform correctness, and final state.

But for register, it has fixed numbers, perhaps we don't need to constraint it like memory, we constraint by all instructions, step by step.

So this is wrong:

At present, there is no constraint on the reading and writing of register

We did constraint register. The register's initial state is all 16 ZEROs, and each instruction changes register.

from olavm.