| Example | Preprocessed Columns | Trace Columns | LogUp Columns |
|---|---|---|---|
| Permutation argument check | • unordered list • ordered list | 1 / unordered list - 1 / ordered list | |
| Range Check (0 ≤ a < 2^bits) | [0,2^bits) rows | • lookup columns • multiplicities column | • 1 / lookup • multiplicity / preprocessed |
| Comparator check (a > b) | [0,2^bits) rows | • a • b • multiplicities column | • 1 / (a - b) • multiplicity / preprocessed |
| IsZero check (a == 0) | • a • a_inv | ||
| XOR operations | valid XOR operations | • lookup columns • multiplicities column | |
| Selectors | columns of 0s and 1s | ||
| Checking whether current row is first row or not | single column (first row = 1, other rows = 0) | ||
| Connecting multiple components (output of Component A is input of Component B) | • 1 / output • 1 / input * (-1) | ||
| Public Input/Output | 1 / input + 1 / output |
AIR Development
Additional examples
Below is a list of additional examples that you can implement as an AIR using S-two, some of which we have already implemented in the previous sections.
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