String-to-String Interpretations With Polynomial-Size Output (Track B: Automata, Logic, Semantics, and Theory of Programming)
Mikołaj Bojańczyk, Sandra Kiefer, Nathan Lhote · arXiv (Cornell University) · 2019
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.