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arXiv · 1905.13190

String-to-String Interpretations with Polynomial-Size Output

Mikołaj Bojańczyk·Sandra Kiefer·Nathan Lhote
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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 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.

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Mikołaj Bojańczyk, Sandra Kiefer, Nathan Lhote. 2019-05-30. String-to-String Interpretations with Polynomial-Size Output. https://arxiv.org/abs/1905.13190

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