Struct MinimumAxiomSet 

pub struct MinimumAxiomSet { /* private fields */ }

The Minimum Axiom Set problem.

Given a set of sentences S = {0, ..., num_sentences - 1}, a subset T ⊆ S of true sentences, and a list of implications where each implication (A, c) means “if all sentences in A hold, then c holds”, find a smallest subset S₀ ⊆ T whose deductive closure under the implications equals T.

Representation

Each true sentence has a binary variable: config[i] = 1 if true_sentences[i] is selected as an axiom, 0 otherwise. The configuration space is vec![2; |T|].

Example

use problemreductions::models::misc::MinimumAxiomSet;
use problemreductions::{Problem, Solver, BruteForce};

// 8 sentences, all true, with implications forming a cycle
let problem = MinimumAxiomSet::new(
    8,
    vec![0, 1, 2, 3, 4, 5, 6, 7],
    vec![
        (vec![0], 2), (vec![0], 3),
        (vec![1], 4), (vec![1], 5),
        (vec![2, 4], 6), (vec![3, 5], 7),
        (vec![6, 7], 0), (vec![6, 7], 1),
    ],
);
let solver = BruteForce::new();
let solution = solver.find_witness(&problem);
assert!(solution.is_some());

Implementations

impl MinimumAxiomSet

pub fn new( num_sentences: usize, true_sentences: Vec<usize>, implications: Vec<(Vec<usize>, usize)>, ) -> Self

Create a new Minimum Axiom Set instance.

Panics

Panics if any true sentence index is out of range, if true sentences contain duplicates, or if any implication references a sentence outside S.

pub fn num_sentences(&self) -> usize

Returns the total number of sentences |S|.

pub fn num_true_sentences(&self) -> usize

Returns the number of true sentences |T|.

pub fn num_implications(&self) -> usize

Returns the number of implications.

pub fn true_sentences(&self) -> &[usize]

Returns the true sentence indices.

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

Returns the implications.

Trait Implementations

impl Clone for MinimumAxiomSet

fn clone(&self) -> MinimumAxiomSet

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for MinimumAxiomSet

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

Formats the value using the given formatter.

impl<'de> Deserialize<'de> for MinimumAxiomSet

fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error>

where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl Problem for MinimumAxiomSet

const NAME: &'static str = "MinimumAxiomSet"

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

type Value = Min<usize>

The evaluation value type.

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

Returns variant attributes derived from type parameters.

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

Configuration space dimensions. Each entry is the cardinality of that variable.

fn evaluate(&self, config: &[usize]) -> Min<usize>

Evaluate the problem on a configuration.

fn num_variables(&self) -> usize

Number of variables (derived from dims).

fn problem_type() -> ProblemType

Look up this problem’s catalog entry.

impl ReduceTo<MinimumAxiomSet> for ExactCoverBy3Sets

type Result = ReductionXC3SToMinimumAxiomSet

The reduction result type.

fn reduce_to(&self) -> Self::Result

Reduce this problem to the target problem type.

impl Serialize for MinimumAxiomSet

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

where __S: Serializer,

Serialize this value into the given Serde serializer.

impl DeclaredVariant for MinimumAxiomSet