maskVars
plain-language theorem explainer
The bitmask variable selector computes the list of variables whose bits are set in the given mask for an n-variable instance. Complexity researchers studying small-bias XOR families cite this when building explicit constraint sets from masks. It is realized by filtering the index range with bit tests.
Claim. For natural numbers $n$ and $m$, let $S(n,m)$ be the list of all indices $i$ in the set from 0 to $n-1$ such that the $i$-th bit of $m$ is set.
background
Variables for an n-variable problem are indices drawn from the finite set of size n. The module supplies placeholder structure for explicit small-bias families of XOR systems. Upstream, a variable is defined as an element of that finite index set, which permits direct lists of selected indices to be assembled via bit tests.
proof idea
The definition generates the complete range of indices from 0 to n-1 and retains only those positions where the corresponding bit in the mask is set, via a direct filter using the bit-test predicate.
why it matters
This definition supplies the variable list to the single-constraint XOR constructor in the same module. It advances the placeholder structure for small-bias families of XOR systems. In the Recognition Science setting such mask selections support compact representations that align with efficient logical encodings.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.