A Comparison of Tree Transductionsde ned by Monadic Second Order
نویسندگان
چکیده
Formulas from monadic second order (mso) logic with one and two free variables can be used to deene the nodes and edges (respectively) of a graph, in terms of a given graph. Such mso deenable 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 deenable tree transductions are exactly those tree transductions that can be computed by attributed tree transducers with look-ahead, which are a speciic type of two-stage attribute grammar: in the rst (look-ahead) stage all attributes have nitely many values, in the second stage all attributes are trees, and the second stage satisses 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.
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