String-to-String Interpretations with Polynomial-Size Output
Abstract
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.
Cite
@article{arxiv.1905.13190,
title = {String-to-String Interpretations with Polynomial-Size Output},
author = {Mikołaj Bojańczyk and Sandra Kiefer and Nathan Lhote},
journal= {arXiv preprint arXiv:1905.13190},
year = {2019}
}
Comments
35 pages, full version of a paper accepted for the 46th International Colloquium on Automata, Languages and Programming (ICALP 2019)