# Constructing a BPE Tokenization DFA

arXiv: https://arxiv.org/abs/2405.07671 · HTML: https://mlsanity.com/paper/2405.07671/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 14 references that are in the map.
- First posted on arXiv 13 May 2024.

## Builds on (most cited first, 3 of 3)

- [Neural Machine Translation of Rare Words with Subword Units](https://mlsanity.com/paper/1508.07909/) (2015)
- [SentencePiece: A simple and language independent subword tokenizer and detokenizer for Neural Text Processing](https://mlsanity.com/paper/1808.06226/) (2018)
- [Glitch Tokens in Large Language Models: Categorization Taxonomy and Effective Detection](https://mlsanity.com/paper/2404.09894/) (2024)

## Built on by (most cited first, 5 of 5)

- [Syntactic and Semantic Control of Large Language Models via Sequential Monte Carlo](https://mlsanity.com/paper/2504.13139/) (2025)
- [The Foundations of Tokenization: Statistical and Computational Concerns](https://mlsanity.com/paper/2407.11606/) (2024)
- [Transducing Language Models](https://mlsanity.com/paper/2603.05193/) (2026)
- [On the Proper Treatment of Units in Surprisal Theory](https://mlsanity.com/paper/2604.28147/) (2026)
- [Length-MAX Tokenizer for Language Models](https://mlsanity.com/paper/2511.20849/) (2025)

## Abstract (arXiv)

Many natural language processing systems operate over tokenizations of text to address the open-vocabulary problem. In this paper, we give and analyze an algorithm for the efficient construction of deterministic finite automata (DFA) designed to operate directly on tokenizations produced by the popular byte pair encoding (BPE) technique. This makes it possible to apply many existing techniques and algorithms to the tokenized case, such as pattern matching, equivalence checking of tokenization dictionaries, and composing tokenized languages in various ways. The construction preserves some key properties of the automaton, and we use this to establish asymptotic bounds on the state complexity of the automata that result. Finally, we demonstrate how to construct an input-deterministic (subsequential) string-to-string transducer which precisely describes the relationship between strings and their correct tokenizations.