## Rustfst

Rust implementation of Weighted Finite States Transducers.

Rustfst is a library for constructing, combining, optimizing, and searching weighted finite-state transducers (FSTs). Weighted finite-state transducers are automata where each transition has an input label, an output label, and a weight. The more familiar finite-state acceptor is represented as a transducer with each transition's input and output label equal. Finite-state acceptors are used to represent sets of strings (specifically, regular or rational sets); finite-state transducers are used to represent binary relations between pairs of strings (specifically, rational transductions). The weights can be used to represent the cost of taking a particular transition.

FSTs have key applications in speech recognition and synthesis, machine translation, optical character recognition, pattern matching, string processing, machine learning, information extraction and retrieval among others. Often a weighted transducer is used to represent a probabilistic model (e.g., an n-gram model, pronunciation model). FSTs can be optimized by determinization and minimization, models can be applied to hypothesis sets (also represented as automata) or cascaded by finite-state composition, and the best results can be selected by shortest-path algorithms.

## References

Implementation heavily inspired from Mehryar Mohri's, Cyril Allauzen's and Michael Riley's work :

- Weighted automata algorithms
- The design principles of a weighted finite-state transducer library
- OpenFst: A general and efficient weighted finite-state transducer library
- Weighted finite-state transducers in speech recognition

## Example

```
use anyhow::Result;
use rustfst::prelude::*;
use rustfst::algorithms::determinize::{DeterminizeType, determinize};
use rustfst::algorithms::rm_epsilon::rm_epsilon;
use std::sync::Arc;
fn main() -> Result<()> {
// Creates a empty wFST
let mut fst = VectorFst::<TropicalWeight>::new();
// Add some states
let s0 = fst.add_state();
let s1 = fst.add_state();
let s2 = fst.add_state();
// Set s0 as the start state
fst.set_start(s0)?;
// Add a transition from s0 to s1
fst.add_tr(s0, Tr::new(3, 5, 10.0, s1))?;
// Add a transition from s0 to s2
fst.add_tr(s0, Tr::new(5, 7, 18.0, s2))?;
// Set s1 and s2 as final states
fst.set_final(s1, 31.0)?;
fst.set_final(s2, 45.0)?;
// Iter over all the paths in the wFST
for p in fst.paths_iter() {
println!("{:?}", p);
}
// A lot of operations are available to modify/optimize the FST.
// Here are a few examples :
// - Remove useless states.
connect(&mut fst)?;
// - Optimize the FST by merging states with the same behaviour.
minimize(&mut fst, true)?;
// - Copy all the input labels in the output.
project(&mut fst, ProjectType::ProjectInput);
// - Remove epsilon transitions.
rm_epsilon(&mut fst)?;
// - Compute an equivalent FST but deterministic.
fst = determinize(Arc::new(fst), DeterminizeType::DeterminizeFunctional)?;
Ok(())
}
```

## Status

A big number of algorithms are already implemented. The main one missing is the Composition.

## Benchmark with OpenFST

I did a benchmark some time ago on almost every linear fst algorithm and compared the results with `OpenFst`

. You can find the results here :

Spoiler alert: `Rustfst`

is faster on all those algorithms

For the other algorithms, i'm finishing the implementation then will do another round of benchmarks.

At the moment, the main algorithm missing in `Rustfst`

is the composition that will be implemented shortly. All the important algorithms like minimization, determinization ... are already implemented but not benched and thus not (necessarily) optimized.

## Documentation

The documentation of the last released version is available here : https://docs.rs/rustfst

## License

Licensed under either of

- Apache License, Version 2.0 (LICENSE-APACHE or http://www.apache.org/licenses/LICENSE-2.0)
- MIT license (LICENSE-MIT) or http://opensource.org/licenses/MIT)

at your option.

## Contribution

Unless you explicitly state otherwise, any contribution intentionally submitted for inclusion in the work by you, as defined in the Apache-2.0 license, shall be dual licensed as above, without any additional terms or conditions.