# Single use register automata for data words

## TL;DR

This paper investigates single-use register automata for data words, demonstrating their increased robustness and equivalence across multiple models, and establishing a solid algebraic and transducer theory.

## Contribution

It introduces the single-use restriction in register automata, showing that it unifies various models and enables algebraic and transducer theories for data words.

## Key findings

- Five automata models are equivalent under the single-use restriction.
- A version of Krohn-Rhodes Theorem applies to these automata.
- A robust theory of transducers with four equivalent models is developed.

## Abstract

Our starting point are register automata for data words, in the style of Kaminski and Francez. We study the effects of the single-use restriction, which says that a register is emptied immediately after being used. We show that under the single-use restriction, the theory of automata for data words becomes much more robust. The main results are: (a) five different machine models are equivalent as language acceptors, including one-way and two-way single-use register automata; (b) one can recover some of the algebraic theory of languages over finite alphabets, including a version of the Krohn-Rhodes Theorem; (c) there is also a robust theory of transducers, with four equivalent models, including two-way single use transducers and a variant of streaming string transducers for data words. These results are in contrast with automata for data words without the single-use restriction, where essentially all models are pairwise non-equivalent.