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String-to-String Interpretations With Polynomial-Size Output (Track B: Automata, Logic, Semantics, and Theory of Programming)

Authors Mikołaj Bojańczyk, Sandra Kiefer, Nathan Lhote

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ACM Subject Classification
  • Theory of computation → Transducers
Keywords
  • MSO
  • interpretations
  • pebble transducers
  • polyregular functions

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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 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.

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Mikołaj Bojańczyk, Sandra Kiefer, and Nathan Lhote. String-to-String Interpretations With Polynomial-Size Output (Track B: Automata, Logic, Semantics, and Theory of Programming). In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 106:1-106:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.ICALP.2019.106

Author Details

Mikołaj Bojańczyk
  • Institute of Informatics, University of Warsaw, Poland
Sandra Kiefer
  • Department of Computer Science, RWTH Aachen University, Germany
Nathan Lhote
  • Institute of Informatics, University of Warsaw, Poland

Acknowledgements

The authors would like to thank Benedikt Brütsch for helpful discussions on the topic.

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