Constructing a BPE Tokenization DFA
This work provides a foundational tool for NLP systems using BPE, allowing integration of automata-based techniques into tokenized text processing.
The paper tackles the problem of efficiently constructing deterministic finite automata (DFA) for byte pair encoding (BPE) tokenizations, enabling applications like pattern matching and equivalence checking, and establishes asymptotic bounds on state complexity.
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.