Abstract. Formulas from monadic second order (mso) logic with one and two free variables can be used to define the nodes and edges (respectively) of a graph, in terms of a given graph. Such mso definable graph transductions play a role in the theory of graph grammars. Here we investigate the special case of trees. The main result is that the mso definable tree transductions are exactly those tree transductions that can be computed by attributed tree transducers with look-ahead, which are a specific type of two-stage attribute grammar: in the first (look-ahead) stage all attributes have finitely many values, in the second stage all attributes are trees, and the second stage satisfies the single use restriction (i.e., each attribute is used at most once). Moreover, if we allow the mso transductions to produce trees with shared subtrees (i.e., term graphs, that have to be unfolded), then the single use restriction can be dropped. 1
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