# Formal Languages and TQFTs with Defects

arXiv: https://arxiv.org/abs/2412.09688 · HTML: https://mlsanity.com/paper/2412.09688/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 21 references that are in the map.
- First posted on arXiv 12 Dec 2024.

## Builds on (most cited first, 2 of 2)

- [The categorical contours of the Chomsky-Sch"utzenberger representation theorem](https://mlsanity.com/paper/2405.14703/) (2023)
- [Tensor Product Representations of Subregular Formal Languages](https://mlsanity.com/paper/1908.08132/) (2019)

## Abstract (arXiv)

A construction that assigns a Boolean 1D TQFT with defects to a finite state automaton was recently developed by Gustafson, Im, Kaldawy, Khovanov, and Lihn. We show that the construction is functorial with respect to the category of finite state automata with transducers as morphisms. Certain classes of subregular languages correspond to additional cohomological structures on the associated TQFTs. We also show that the construction generalizes to context-free grammars through a categorical version of the Chomsky-Sch"utzenberger representation theorem, due to Melli`es and Zeilberger. The corresponding TQFTs are then described as morphisms of colored operads on an operad of cobordisms with defects.