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use proptest::{prelude::*, *};
use rand::{distributions::Bernoulli, seq::SliceRandom};
use crate::{cnf::CnfFormula, lit::Lit};
/// Generate small hard unsat instances.
///
/// Implementation of http://www.cs.qub.ac.uk/~i.spence/sgen/ but with random partitions
pub fn sgen_unsat_formula(
blocks: impl Strategy<Value = usize>,
) -> impl Strategy<Value = CnfFormula> {
blocks.prop_flat_map(|blocks| {
collection::vec(bool::ANY, blocks * 4 + 1).prop_perturb(|polarity, mut rng| {
let mut clauses: Vec<Vec<Lit>> = vec![];
let mut lits = polarity
.into_iter()
.enumerate()
.map(|(index, polarity)| Lit::from_index(index, polarity))
.collect::<Vec<_>>();
for &invert in [false, true].iter() {
lits.shuffle(&mut rng);
for block in lits.chunks_exact(4) {
for a in 0..4 {
for b in 0..a {
for c in 0..b {
let mut clause =
vec![block[a] ^ invert, block[b] ^ invert, block[c] ^ invert];
clause.shuffle(&mut rng);
clauses.push(clause);
}
}
}
}
let &lit_a = lits.last().unwrap();
for b in 0..4 {
for c in 0..b {
let mut clause = vec![lit_a ^ invert, lits[b] ^ invert, lits[c] ^ invert];
clause.shuffle(&mut rng);
clauses.push(clause);
}
}
}
clauses.shuffle(&mut rng);
CnfFormula::from(clauses)
})
})
}
/// Generate a sat instance.
///
/// This generates a random full assignment and then only generates clauses compatible with that
/// assignment.
pub fn sat_formula(
vars: impl Strategy<Value = usize>,
clause_count: impl Strategy<Value = usize>,
density: impl Strategy<Value = f64>,
polarity_dist: impl Strategy<Value = f64>,
) -> impl Strategy<Value = CnfFormula> {
(vars, clause_count, density, polarity_dist).prop_flat_map(
|(vars, clause_count, density, polarity_dist)| {
let density = Bernoulli::new(density).unwrap();
let polarity_dist = Bernoulli::new(polarity_dist).unwrap();
collection::vec(bool::ANY, vars).prop_perturb(move |polarity, mut rng| {
let mut clauses: Vec<Vec<Lit>> = vec![];
let lits = polarity
.into_iter()
.enumerate()
.map(|(index, polarity)| Lit::from_index(index, polarity))
.collect::<Vec<_>>();
for _ in 0..clause_count {
let &fixed_lit = lits.choose(&mut rng).unwrap();
let mut clause = vec![fixed_lit];
for &lit in lits.iter() {
if lit != fixed_lit && rng.sample(density) {
clause.push(lit ^ rng.sample(polarity_dist));
}
}
clause.shuffle(&mut rng);
clauses.push(clause);
}
clauses.shuffle(&mut rng);
CnfFormula::from(clauses)
})
},
)
}
/// Generates a conditional pigeon hole principle formula.
pub fn conditional_pigeon_hole(
columns: impl Strategy<Value = usize>,
extra_rows: impl Strategy<Value = usize>,
) -> impl Strategy<Value = (Vec<Lit>, usize, CnfFormula)> {
(columns, extra_rows).prop_flat_map(|(columns, extra_rows)| {
let rows = columns + extra_rows;
let vars = (columns + 1) * rows;
collection::vec(bool::ANY, vars).prop_perturb(move |polarity, mut rng| {
let mut clauses: Vec<Vec<Lit>> = vec![];
let lits = polarity
.into_iter()
.enumerate()
.map(|(index, polarity)| Lit::from_index(index, polarity))
.collect::<Vec<_>>();
for i in 1..columns + 1 {
for j in 0..rows {
for k in 0..j {
let mut clause = [lits[i * rows + j], lits[i * rows + k]];
clause.shuffle(&mut rng);
clauses.push(clause[..].to_owned());
}
}
}
for j in 0..rows {
let mut clause: Vec<_> = (0..columns + 1).map(|i| !lits[i * rows + j]).collect();
clause.shuffle(&mut rng);
clauses.push(clause[..].to_owned());
}
clauses.shuffle(&mut rng);
(lits[0..rows].to_owned(), columns, CnfFormula::from(clauses))
})
})
}
|
