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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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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.

Cite AsGet BibTex

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

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.

Subject Classification

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

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References

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