# Tutorial: varphi-Transductions in OpenFst via the Gallic Semiring

arXiv: https://arxiv.org/abs/2506.17942 · HTML: https://mlsanity.com/paper/2506.17942/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 3 references that are in the map.
- First posted on arXiv 22 Jun 2025.

## Builds on (most cited first, 1 of 1)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)

## Abstract (arXiv)

OpenFst, a popular finite-state transducer library, supports varphi-transitions but, due to an implementation constraint, they cannot be used with transducers in a straightforward way. In this short tutorial, we describe how one can use other functionality provided by OpenFst (namely, the Gallic semiring) to correctly implement varphi-transductions and demonstrate it by implementing the MaxMatch (WordPiece) tokenization algorithm (Devlin et al., 2019; Song et al., 2021). Accompanying self-contained code examples are provided. https://www.openfst.org/twiki/pub/Contrib/FstContrib/phitransductiontutorialcode.tgz