Enum CubeStructure 

pub enum CubeStructure {
    Constant(bool),
    Junta {
        relevant: Vec<usize>,
        subtable: Vec<bool>,
    },
    Affine {
        coeffs: Vec<bool>,
        constant: bool,
    },
    Symmetric {
        by_weight: Vec<bool>,
    },
    LowDegree {
        degree: usize,
        anf: Vec<bool>,
    },
    ResistedArsenal {
        nonlinearity: u64,
        degree: usize,
    },
}

The compressibility class of a Boolean function on the hypercube, tightest description first. Each variant carries a re-checkable witness (CubeStructure::reconstruct) except the residue.

Variants

Constant(bool)

Every corner carries the same value — the whole cube in one bit.

Junta

A junta: the output depends only on relevant (a strict subset of the variables); subtable is its 2^{|relevant|} truth table over those variables (indexed LSB-first in relevant order).

Fields

relevant: Vec<usize>

subtable: Vec<bool>

Affine

Affine (degree ≤ 1): f(x) = ⊕ᵢ coeffs[i]·xᵢ ⊕ constant.

Fields

coeffs: Vec<bool>

constant: bool

Symmetric

Symmetric: the output depends only on the Hamming weight of the input; by_weight[w] is its value on every corner of weight w (length n+1).

Fields

by_weight: Vec<bool>

LowDegree

Low algebraic degree with a sparse ANF: anf is the 2ⁿ Möbius-transform witness, degree its top.

Fields

degree: usize

anf: Vec<bool>

ResistedArsenal

No lens compresses it: dense high-degree ANF, all variables relevant, high nonlinearity. The incompressible residue relative to this arsenal — NOT a proof of structurelessness (Chaitin).

Fields

nonlinearity: u64

degree: usize

Implementations

impl CubeStructure

pub fn reconstruct(&self, n: usize) -> Option<Vec<bool>>

Rebuild the 2ⁿ truth table from this description — the re-checkable decode witness. None for the residue (which carries no compressed description) or a malformed witness.

Trait Implementations

impl Clone for CubeStructure

fn clone(&self) -> CubeStructure

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for CubeStructure

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl PartialEq for CubeStructure

fn eq(&self, other: &CubeStructure) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl Eq for CubeStructure

impl StructuralPartialEq for CubeStructure