Struct Satisfiability 

pub struct Satisfiability { /* private fields */ }

Boolean Satisfiability (SAT) problem in CNF form.

Given a Boolean formula in conjunctive normal form (CNF), determine if there exists an assignment that satisfies all clauses. This is the decision version of the problem.

Example

use problemreductions::models::formula::{Satisfiability, CNFClause};
use problemreductions::{Problem, Solver, BruteForce};

// Formula: (x1 OR x2) AND (NOT x1 OR x3) AND (NOT x2 OR NOT x3)
let problem = Satisfiability::new(
    3,
    vec![
        CNFClause::new(vec![1, 2]),      // x1 OR x2
        CNFClause::new(vec![-1, 3]),     // NOT x1 OR x3
        CNFClause::new(vec![-2, -3]),    // NOT x2 OR NOT x3
    ],
);

let solver = BruteForce::new();
let solutions = solver.find_all_satisfying(&problem);

// Verify solutions satisfy all clauses
for sol in solutions {
    assert!(problem.evaluate(&sol));
}

Implementations

impl Satisfiability

pub fn new(num_vars: usize, clauses: Vec<CNFClause>) -> Self

Create a new SAT problem.

pub fn num_vars(&self) -> usize

Get the number of variables.

pub fn num_clauses(&self) -> usize

Get the number of clauses.

pub fn num_literals(&self) -> usize

Get the total number of literal occurrences across all clauses.

pub fn clauses(&self) -> &[CNFClause]

Get the clauses.

pub fn get_clause(&self, index: usize) -> Option<&CNFClause>

Get a specific clause.

pub fn count_satisfied(&self, assignment: &[bool]) -> usize

Count satisfied clauses for an assignment.

pub fn is_satisfying(&self, assignment: &[bool]) -> bool

Check if an assignment satisfies all clauses.

pub fn is_valid_solution(&self, config: &[usize]) -> bool

Check if a solution (config) is valid.

For SAT, a valid solution is one that satisfies all clauses.

Trait Implementations

impl Clone for Satisfiability

fn clone(&self) -> Satisfiability

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for Satisfiability

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

Formats the value using the given formatter.

impl<'de> Deserialize<'de> for Satisfiability

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

where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl Problem for Satisfiability

const NAME: &'static str = "Satisfiability"

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

type Metric = bool

The evaluation metric type.

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

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

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

Evaluate the problem on a configuration.

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

Returns variant attributes derived from type parameters.

fn num_variables(&self) -> usize

Number of variables (derived from dims).

impl ReduceTo<CircuitSAT> for Satisfiability

type Result = ReductionSATToCircuit

The reduction result type.

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

Reduce this problem to the target problem type.

impl ReduceTo<KColoring<K3, SimpleGraph>> for Satisfiability

type Result = ReductionSATToColoring

The reduction result type.

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

Reduce this problem to the target problem type.

impl ReduceTo<KSatisfiability<K3>> for Satisfiability

type Result = ReductionSATToKSAT<K3>

The reduction result type.

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

Reduce this problem to the target problem type.

impl ReduceTo<MaximumIndependentSet<SimpleGraph, One>> for Satisfiability

type Result = ReductionSATToIS

The reduction result type.

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

Reduce this problem to the target problem type.

impl ReduceTo<MinimumDominatingSet<SimpleGraph, i32>> for Satisfiability

type Result = ReductionSATToDS

The reduction result type.

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

Reduce this problem to the target problem type.

impl ReduceTo<Satisfiability> for KSatisfiability<K2>

type Result = ReductionKSATToSAT<K2>

The reduction result type.

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

Reduce this problem to the target problem type.

impl ReduceTo<Satisfiability> for KSatisfiability<K3>

type Result = ReductionKSATToSAT<K3>

The reduction result type.

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

Reduce this problem to the target problem type.

impl ReduceTo<Satisfiability> for KSatisfiability<KN>

type Result = ReductionKSATToSAT<KN>

The reduction result type.

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

Reduce this problem to the target problem type.

impl Serialize for Satisfiability

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 Satisfiability

impl SatisfactionProblem for Satisfiability