Struct AlgebraicEquationsOverGF2 

pub struct AlgebraicEquationsOverGF2 { /* private fields */ }

Algebraic Equations over GF(2).

Given m multilinear polynomials over GF(2) in n variables, determine whether there exists an assignment of the variables making all polynomials evaluate to 0 (mod 2).

Each equation is a list of monomials. Each monomial is a sorted list of variable indices (0-indexed). An empty monomial represents the constant 1. A polynomial evaluates to 0 when the XOR (sum mod 2) of all its monomial values equals 0.

Example

use problemreductions::models::algebraic::AlgebraicEquationsOverGF2;
use problemreductions::{Problem, BruteForce};

// Two equations in 3 variables:
//   x0*x1 + x2 = 0 (mod 2)
//   x0 + 1 = 0 (mod 2)
let problem = AlgebraicEquationsOverGF2::new(
    3,
    vec![
        vec![vec![0, 1], vec![2]],   // x0*x1 XOR x2
        vec![vec![0], vec![]],        // x0 XOR 1
    ],
).unwrap();

let solver = BruteForce::new();
let witness = solver.solve(&problem).unwrap();
assert!(witness.is_some());

Implementations

impl AlgebraicEquationsOverGF2

pub fn new( num_variables: usize, equations: Vec<Vec<Vec<usize>>>, ) -> Result<Self, ConstructionError>

Create a new AlgebraicEquationsOverGF2 instance.

Returns an error if any variable index is out of range or any monomial is not strictly sorted.

pub fn num_variables(&self) -> usize

Get the number of variables.

pub fn num_equations(&self) -> usize

Get the number of equations.

pub fn equations(&self) -> &[Vec<Vec<usize>>]

Get the equations.

Trait Implementations

impl BruteForceProblem for AlgebraicEquationsOverGF2

fn dimensions(&self) -> Vec<usize>

Cardinality of each coordinate in the brute-force search space.

fn num_variables(&self) -> usize

Number of coordinates in the brute-force search space.

impl Clone for AlgebraicEquationsOverGF2

fn clone(&self) -> AlgebraicEquationsOverGF2

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for AlgebraicEquationsOverGF2

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

Formats the value using the given formatter.

impl DeclaredVariant for AlgebraicEquationsOverGF2

impl<'de> Deserialize<'de> for AlgebraicEquationsOverGF2

fn deserialize<D>(deserializer: D) -> Result<Self, D::Error>

where D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl Problem for AlgebraicEquationsOverGF2

const NAME: &'static str = "AlgebraicEquationsOverGF2"

Base name of this problem type (e.g., “MaximumIndependentSet”).

type Solution = Vec<bool>

Mathematical witness type for this problem.

type Value = Or

The evaluation value type.

fn parameter_names() -> &'static [&'static str]

Canonical parameter names for this problem model.

fn parameters(&self) -> ProblemParameters

Measure the complete canonical parameters of this concrete instance.

fn variant() -> Vec<(&'static str, &'static str)>

Returns variant attributes derived from type parameters.

fn evaluate(&self, config: &Self::Solution) -> Result<Or, EvaluationError>

Evaluate the problem on a solution.

fn problem_type() -> ProblemType

Look up this problem’s catalog entry.

impl ReduceTo<AlgebraicEquationsOverGF2> for ExactCoverBy3Sets

type Result = ReductionX3CToAlgebraicEquationsOverGF2

The reduction result type.

fn reduce_to(&self) -> Result<Self::Result, ReductionError>

Reduce this problem to the target problem type.

fn target_construction(error: ConstructionError) -> ReductionError

where Self: Sized,

Attach this reduction edge to a target-construction failure.

fn exact_i64( value: usize, operation: impl Into<String>, ) -> Result<i64, ReductionError>

where Self: Sized,

Convert a structural count used by the target’s exact integer algebra.

impl Serialize for AlgebraicEquationsOverGF2

fn serialize<__S>(&self, __serializer: __S) -> Result<__S::Ok, __S::Error>

where __S: Serializer,

Serialize this value into the given Serde serializer.