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23

The oracle is basically just an implementation of the predicate you want to search for a satisfying solution to. For example, suppose you have a 3-sat problem: (¬x1 ∨ ¬x3 ∨ ¬x4) ∧ (x2 ∨ x3 ∨ ¬x4) ∧ (x1 ∨ ¬x2 ∨ x4) ∧ (x1 ∨ x3 ∨ x4) ∧ (¬x1 ∨ x2 ∨ ¬x3) Or, in table form with each row being a 3-clause, x meaning "this variable false", o ...

4

The work of Berman, Raskhodnikova, and Yaroslavtsev  introduces testing of functions $f\colon [n]^d\to \mathbb{R}$ with regard to $L_p$ distances, for $p\geq 1$. It is meant to capture situations where the magnitude of the noise is what matters (rather than the more brittle Hamming distance). (Some results pertaining to $L_p$ distances can also be found ...

3

Your problem is at least as hard as the NP-hard problem called Minimum Feedback Arc Set. Consider a directed graph and set $f(u,v)=1$ if it contains an arc from $u$ to $v$, and $0$ otherwise. Then your problem corresponds to finding a minimum feedback arc set: a minimum set of arcs whose removal yields a directed acyclic graph (DAG). From such a DAG, one ...

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