On the Balancedness of Tree-to-Word Transducers

A language over an alphabet [Formula: see text] of opening ([Formula: see text]) and closing ([Formula: see text]) brackets, is balanced if it is a subset of the Dyck language [Formula: see text] over [Formula: see text], and it is well-formed if all words are prefixes of words in [Formula: see text]. We show that well-formedness of a context-free language is decidable in polynomial time, and that the longest common reduced suffix can be computed in polynomial time. With this at a hand we decide for the class 2-TW of non-linear tree transducers with output alphabet [Formula: see text] whether or not the output language is balanced.