A macro tree transduction is MSO definable if and only if it is of linear size increase. Furthermore, it is decidable for a macro tree transduction whether or not it is MSO definable.
CITATION STYLE
Engelfriet, J., & Maneth, S. (2000). Characterizing and deciding MSO-definability of macro tree transductions. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1770, pp. 542–554). Springer Verlag. https://doi.org/10.1007/3-540-46541-3_45
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