halo2-tutorial VS cairo-lang

As another example, you could define a circuit for proving the N-th Fibonacci number, where row i of the matrix has the values x[i-2], x[i-1], x[i]. This means you'd need three advice columns to begin with, let's call them a, b, c. Then, you'd constrain c to be equal to a + b in the same row using a gate, which requires adding a selector column for controlling it. And you'd have to set up equality constraints so that a and b are equal to b and c from the previous row. Last, in order to expose the N-th number as a public value, you'd need an instance column, constrained to equal the value of c at the last row.

This also means that, if you want to define specific thresholds for your integer variables, you'll need to add extra constraints for it. Some languages like Noir will do it for you, whereas others will require you to do it manually.