2019/05/30 by Bojańczyk, Mikołaj, Kiefer, Sandra, Lhote, Nathan · 3 citations
#FOS: Computer and information sciences #Formal Languages and Automata Theory (cs.FL) #Logic in Computer Science (cs.LO)
paper · doi:10.48550/arxiv.1905.13190
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.