# String-to-String Interpretations with Polynomial-Size Output

arXiv: https://arxiv.org/abs/1905.13190 · HTML: https://mlsanity.com/paper/1905.13190/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 May 2019.

## Built on by (most cited first, 1 of 1)

- [Learning Transductions and Alignments with RNN Seq2seq Models](https://mlsanity.com/paper/2303.06841/) (2023)

## Abstract (arXiv)

String-to-string MSO interpretations are like Courcelle's MSO transductions, except that a single output position can be represented using a tuple of input positions instead of just a single input position. In particular, the output length is polynomial in the input length, as opposed to MSO transductions, which have output of linear length. We show that string-to-string MSO interpretations are exactly the polyregular functions. The latter class has various characterizations, one of which is that it consists of the string-to-string functions recognized by pebble transducers. Our main result implies the surprising fact that string-to-string MSO interpretations are closed under composition.