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use std::cmp::Ordering;
use std::collections::VecDeque;
use anyhow::Result;
use crate::fst_traits::ExpandedFst;
use crate::semirings::Semiring;
use crate::{StateId, Tr, Trs, KDELTA};
use std::marker::PhantomData;
struct Isomorphism<'a, W: Semiring, F1: ExpandedFst<W>, F2: ExpandedFst<W>> {
fst_1: &'a F1,
fst_2: &'a F2,
state_pairs: Vec<Option<StateId>>,
queue: VecDeque<(StateId, StateId)>,
w: PhantomData<W>,
delta: f32,
}
pub fn tr_compare<W: Semiring>(tr_1: &Tr<W>, tr_2: &Tr<W>) -> Ordering {
if tr_1.ilabel < tr_2.ilabel {
return Ordering::Less;
}
if tr_1.ilabel > tr_2.ilabel {
return Ordering::Greater;
}
if tr_1.olabel < tr_2.olabel {
return Ordering::Less;
}
if tr_1.olabel > tr_2.olabel {
return Ordering::Greater;
}
if tr_1.weight < tr_2.weight {
return Ordering::Less;
}
if tr_1.weight > tr_2.weight {
return Ordering::Greater;
}
if tr_1.nextstate < tr_2.nextstate {
return Ordering::Less;
}
if tr_1.nextstate > tr_2.nextstate {
return Ordering::Greater;
}
Ordering::Equal
}
impl<'a, W: Semiring, F1: ExpandedFst<W>, F2: ExpandedFst<W>> Isomorphism<'a, W, F1, F2> {
fn new(fst_1: &'a F1, fst_2: &'a F2, delta: f32) -> Self {
Self {
fst_1,
fst_2,
state_pairs: vec![None; fst_1.num_states()],
queue: VecDeque::new(),
w: PhantomData,
delta,
}
}
fn pair_state(&mut self, s1: StateId, s2: StateId) -> bool {
if self.state_pairs[s1 as usize] == Some(s2) {
return true;
} else if self.state_pairs[s1 as usize].is_some() {
return false;
}
self.state_pairs[s1 as usize] = Some(s2);
self.queue.push_back((s1, s2));
true
}
fn ismorphic_state(&mut self, s1: StateId, s2: StateId) -> Result<bool> {
let fw1 = self.fst_1.final_weight(s1)?;
let fw2 = self.fst_2.final_weight(s2)?;
let fw_equal = match (fw1, fw2) {
(Some(w1), Some(w2)) => w1.approx_equal(w2, self.delta),
(Some(_), None) => false,
(None, Some(_)) => false,
(None, None) => true,
};
if !fw_equal {
return Ok(false);
}
let ntrs1 = self.fst_1.num_trs(s1)?;
let ntrs2 = self.fst_2.num_trs(s2)?;
if ntrs1 != ntrs2 {
return Ok(false);
}
let trs1_owner = self.fst_1.get_trs(s1)?;
let mut trs1: Vec<_> = trs1_owner.trs().iter().collect();
let trs2_owner = self.fst_2.get_trs(s2)?;
let mut trs2: Vec<_> = trs2_owner.trs().iter().collect();
trs1.sort_by(|a, b| tr_compare(a, b));
trs2.sort_by(|a, b| tr_compare(a, b));
for i in 0..trs1.len() {
let arc1 = trs1[i];
let arc2 = trs2[i];
if arc1.ilabel != arc2.ilabel {
return Ok(false);
}
if arc1.olabel != arc2.olabel {
return Ok(false);
}
if !(arc1.weight.approx_equal(&arc2.weight, self.delta)) {
return Ok(false);
}
if !(self.pair_state(arc1.nextstate, arc2.nextstate)) {
return Ok(false);
}
if i > 0 {
let arc0 = trs1[i - 1];
if arc1.ilabel == arc0.ilabel
&& arc1.olabel == arc0.olabel
&& arc1.weight.approx_equal(&arc0.weight, self.delta)
{
bail!("Isomorphic: Non-determinism as an unweighted automaton")
}
}
}
Ok(true)
}
fn isomorphic(&mut self) -> Result<bool> {
if self.fst_1.start().is_none() && self.fst_2.start().is_none() {
return Ok(true);
}
if self.fst_1.start().is_none() || self.fst_2.start().is_none() {
return Ok(false);
}
self.pair_state(self.fst_1.start().unwrap(), self.fst_2.start().unwrap());
while !self.queue.is_empty() {
let (s1, s2) = self.queue.pop_front().unwrap();
if !self.ismorphic_state(s1, s2)? {
return Ok(false);
}
}
Ok(true)
}
}
pub struct IsomorphicConfig {
delta: f32,
}
impl Default for IsomorphicConfig {
fn default() -> Self {
Self { delta: KDELTA }
}
}
impl IsomorphicConfig {
pub fn new(delta: f32) -> Self {
Self { delta }
}
}
pub fn isomorphic<W, F1, F2>(fst_1: &F1, fst_2: &F2) -> Result<bool>
where
W: Semiring,
F1: ExpandedFst<W>,
F2: ExpandedFst<W>,
{
isomorphic_with_config(fst_1, fst_2, IsomorphicConfig::default())
}
pub fn isomorphic_with_config<W, F1, F2>(
fst_1: &F1,
fst_2: &F2,
config: IsomorphicConfig,
) -> Result<bool>
where
W: Semiring,
F1: ExpandedFst<W>,
F2: ExpandedFst<W>,
{
let mut iso = Isomorphism::new(fst_1, fst_2, config.delta);
iso.isomorphic()
}
#[cfg(test)]
mod test {
use super::*;
use crate::fst_impls::VectorFst;
use crate::fst_traits::{MutableFst, SerializableFst};
use crate::semirings::{LogWeight, Semiring};
use crate::Tr;
#[test]
fn test_isomorphic_1() -> Result<()> {
let fst_1: VectorFst<LogWeight> = SerializableFst::from_text_string(
"0\t1\t12\t25\n\
1\n",
)?;
let mut fst_2 = fst_1.clone();
assert!(isomorphic(&fst_1, &fst_2)?);
fst_2.add_tr(0, Tr::new(33, 45, LogWeight::new(0.3), 1))?;
assert!(!isomorphic(&fst_1, &fst_2)?);
Ok(())
}
#[test]
fn test_isomorphic_2() -> Result<()> {
let fst_1: VectorFst<LogWeight> = SerializableFst::from_text_string(
"0\t1\t12\t25\n\
1\n",
)?;
let fst_2: VectorFst<LogWeight> = SerializableFst::from_text_string(
"1\t0\t12\t25\n\
0\n",
)?;
assert!(isomorphic(&fst_1, &fst_2)?);
Ok(())
}
}