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 characterisations, one of which is that it consists of the string-to-string functions recognised by pebble transducers. Our main result implies the surprising fact that string-to-string MSO interpretations are closed under composition.
@InProceedings{bojanczyk_et_al:LIPIcs.ICALP.2019.106, author = {Boja\'{n}czyk, Miko{\l}aj and Kiefer, Sandra and Lhote, Nathan}, title = {{String-to-String Interpretations With Polynomial-Size Output}}, booktitle = {46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)}, pages = {106:1--106:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-109-2}, ISSN = {1868-8969}, year = {2019}, volume = {132}, editor = {Baier, Christel and Chatzigiannakis, Ioannis and Flocchini, Paola and Leonardi, Stefano}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.106}, URN = {urn:nbn:de:0030-drops-106821}, doi = {10.4230/LIPIcs.ICALP.2019.106}, annote = {Keywords: MSO, interpretations, pebble transducers, polyregular functions} }
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